task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-mc-pysms-degree-bounds-l1-s0 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 1 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- every vertex has degree between 3 and 4 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is als... | {"vertices": 10, "required_edges": [], "max_degree": 4, "min_degree": 3, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [0, 9], [1, 6], [1, 7], [1, 8], [1, 9], [2, 5], [2, 7], [2, 8], [2, 9], [3, 4], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [5, 6]]} | 1 |
construct-mc-pysms-degree-bounds-l1-s1 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 1 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree between 4 and 5 (inclusive)
- it contains each of the following edges: (1,11), (0,13), (7,9), (1,13), (4,11), (6,9)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, list... | {"vertices": 14, "required_edges": [[1, 11], [0, 13], [7, 9], [1, 13], [4, 11], [6, 9]], "max_degree": 5, "min_degree": 4, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [0, 11], [0, 12], [0, 13], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [3, 8], [3, 10], [3, 11], [3, 12], [3, 13], [4, 8], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 8], [5, 9], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9]]} | 1 |
construct-mc-pysms-degree-bounds-l2-s0 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 2 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree between 1 and 5 (inclusive)
- it contains each of the following edges: (2,8), (2,6), (2,10), (3,8), (0,10)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed once
... | {"vertices": 11, "required_edges": [[2, 8], [2, 6], [2, 10], [3, 8], [0, 10]], "max_degree": 5, "min_degree": 1, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [0, 9], [0, 10], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 8], [4, 9], [4, 10], [5, 6], [5, 7]]} | 1 |
construct-mc-pysms-degree-bounds-l2-s1 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 2 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- every vertex has degree between 4 and 5 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..12, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is a... | {"vertices": 13, "required_edges": [], "max_degree": 5, "min_degree": 4, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 9], [0, 10], [0, 11], [0, 12], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [2, 7], [2, 9], [2, 10], [2, 11], [2, 12], [3, 6], [3, 9], [3, 10], [3, 11], [3, 12], [4, 5], [4, 9], [4, 10], [4, 11], [4, 12], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-degree-bounds-l3-s0 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 3 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree between 4 and 6 (inclusive)
- it contains each of the following edges: (5,6), (3,8), (0,9), (3,7), (3,9), (4,9)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed o... | {"vertices": 11, "required_edges": [[5, 6], [3, 8], [0, 9], [3, 7], [3, 9], [4, 9]], "max_degree": 6, "min_degree": 4, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10]]} | 1 |
construct-mc-pysms-degree-bounds-l3-s1 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 3 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree between 1 and 3 (inclusive)
- it contains each of the following edges: (2,9), (2,11), (2,10)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..11, listed once
Write your fin... | {"vertices": 12, "required_edges": [[2, 9], [2, 11], [2, 10]], "max_degree": 3, "min_degree": 1, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 9], [0, 10], [0, 11], [1, 9], [1, 10], [1, 11], [2, 9], [2, 10], [2, 11], [3, 6], [3, 7], [3, 8], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8]]} | 1 |
construct-mc-pysms-degree-bounds-l4-s0 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 4 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree between 3 and 3 (inclusive)
- it contains each of the following edges: (0,9), (1,10), (2,9)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..11, listed once
Write your fina... | {"vertices": 12, "required_edges": [[0, 9], [1, 10], [2, 9]], "max_degree": 3, "min_degree": 3, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 9], [0, 10], [0, 11], [1, 9], [1, 10], [1, 11], [2, 9], [2, 10], [2, 11], [3, 6], [3, 7], [3, 8], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8]]} | 1 |
construct-mc-pysms-degree-bounds-l4-s1 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 4 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree between 3 and 6 (inclusive)
- it contains each of the following edges: (4,5), (0,10), (2,7), (6,8), (2,8), (1,6), (0,9), (5,8)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in ... | {"vertices": 14, "required_edges": [[4, 5], [0, 10], [2, 7], [6, 8], [2, 8], [1, 6], [0, 9], [5, 8]], "max_degree": 6, "min_degree": 3, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 6], [1, 7], [1, 10], [1, 11], [1, 12], [1, 13], [2, 6], [2, 7], [2, 8], [2, 9], [2, 12], [2, 13], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 5], [4, 7], [4, 9], [4, 11], [4, 12], [4, 13], [5, 6], [5, 8], [5, 10], [5, 11], [5, 13], [6, 8], [6,... | 1 |
construct-mc-pysms-degree-bounds-l5-s0 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 5 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree between 2 and 5 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..14, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is a... | {"vertices": 15, "required_edges": [], "max_degree": 5, "min_degree": 2, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [5, 6], [5, 7], [5, 8], [5, 9], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9]]} | 1 |
construct-mc-pysms-degree-bounds-l5-s1 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 5 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree between 1 and 5 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..14, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is a... | {"vertices": 15, "required_edges": [], "max_degree": 5, "min_degree": 1, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [5, 6], [5, 7], [5, 8], [5, 9], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9]]} | 1 |
construct-mc-pysms-degree-bounds-l5-s2 | construct | mc_pysms_degree_bounds | graph_existence_degree_bounds | graph_theory | competition | 5 | MathConstraint/pysms_degree_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree between 3 and 6 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..11, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is a... | {"vertices": 12, "required_edges": [], "max_degree": 6, "min_degree": 3, "family": "mc_pysms_degree_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11]]} | 1 |
construct-mc-pysms-girth-degree-l1-s0 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 1 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree between 2 and 5 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 11, "required_edges": [], "max_degree": 5, "min_degree": 2, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 9], [0, 10], [1, 8], [1, 10], [2, 7], [2, 10], [3, 6], [3, 10], [4, 5], [4, 8], [4, 9], [5, 6], [5, 7]]} | 1 |
construct-mc-pysms-girth-degree-l1-s1 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 1 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- every vertex has degree between 4 and 4 (inclusive)
- the girth is at least 4: the graph has no cycle of length less than 4 (a graph without cycles qualifies)
- it contains each of the following edges: (0,4), (0,7), (2,4)
Answer format: {"ed... | {"vertices": 8, "required_edges": [[0, 4], [0, 7], [2, 4]], "max_degree": 4, "min_degree": 4, "min_girth": 4, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [0, 6], [0, 7], [1, 4], [1, 5], [1, 6], [1, 7], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]]} | 1 |
construct-mc-pysms-girth-degree-l1-s2 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 1 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- every vertex has degree between 2 and 3 (inclusive)
- the girth is at least 5: the graph has no cycle of length less than 5 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct verti... | {"vertices": 10, "required_edges": [], "max_degree": 3, "min_degree": 2, "min_girth": 5, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [0, 9], [1, 7], [1, 9], [2, 6], [2, 9], [3, 6], [3, 7], [3, 8], [4, 5], [4, 8], [5, 7]]} | 1 |
construct-mc-pysms-girth-degree-l2-s0 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 2 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree between 2 and 5 (inclusive)
- the girth is at least 4: the graph has no cycle of length less than 4 (a graph without cycles qualifies)
- it contains each of the following edges: (2,12), (3,10), (6,9), (3,13), (3,12),... | {"vertices": 15, "required_edges": [[2, 12], [3, 10], [6, 9], [3, 13], [3, 12], [0, 13]], "max_degree": 5, "min_degree": 2, "min_girth": 4, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [5, 8], [5, 9], [6, 8], [6, 9], [7, 8], [7, 9]]} | 1 |
construct-mc-pysms-girth-degree-l2-s1 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 2 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree between 3 and 3 (inclusive)
- the girth is at least 5: the graph has no cycle of length less than 5 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 14, "required_edges": [], "max_degree": 3, "min_degree": 3, "min_girth": 5, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 11], [0, 12], [0, 13], [1, 9], [1, 10], [1, 13], [2, 8], [2, 10], [2, 12], [3, 7], [3, 10], [3, 11], [4, 6], [4, 9], [4, 12], [5, 6], [5, 7], [5, 8], [6, 13], [7, 9], [8, 11]]} | 1 |
construct-mc-pysms-girth-degree-l2-s2 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 2 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- every vertex has degree between 2 and 5 (inclusive)
- the girth is at least 8: the graph has no cycle of length less than 8 (a graph without cycles qualifies)
- it contains each of the following edges: (2,5)
Answer format: {"edges": [[u, v],... | {"vertices": 9, "required_edges": [[2, 5]], "max_degree": 5, "min_degree": 2, "min_girth": 8, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [1, 6], [1, 8], [2, 5], [2, 7], [3, 4], [3, 6], [4, 5]]} | 1 |
construct-mc-pysms-girth-degree-l3-s0 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 3 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 21 vertices 0..20 such that:
- every vertex has degree between 3 and 5 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 21, "required_edges": [], "max_degree": 5, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 18], [0, 19], [0, 20], [1, 16], [1, 17], [1, 20], [2, 15], [2, 17], [2, 19], [3, 14], [3, 17], [3, 18], [4, 13], [4, 16], [4, 19], [5, 12], [5, 16], [5, 18], [6, 11], [6, 15], [6, 18], [7, 10], [7, 14], [7, 19], [8, 9], [8, 13], [8, 14], [9, 12], [9, 15], [9, 20], [10, 11], [10, 12], [11, 13]]} | 1 |
construct-mc-pysms-girth-degree-l3-s1 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 3 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 25 vertices 0..24 such that:
- every vertex has degree between 3 and 4 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 25, "required_edges": [], "max_degree": 4, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 22], [0, 23], [0, 24], [1, 20], [1, 21], [1, 24], [2, 19], [2, 21], [2, 23], [3, 17], [3, 18], [3, 24], [4, 16], [4, 18], [4, 23], [5, 15], [5, 17], [5, 19], [6, 13], [6, 14], [6, 22], [7, 11], [7, 12], [7, 21], [8, 10], [8, 12], [8, 19], [8, 24], [9, 10], [9, 11], [9, 15], [10, 14], [10, 16], [11, 18], ... | 1 |
construct-mc-pysms-girth-degree-l3-s2 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 3 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 21 vertices 0..20 such that:
- every vertex has degree between 4 and 6 (inclusive)
- the girth is at least 5: the graph has no cycle of length less than 5 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 21, "required_edges": [], "max_degree": 6, "min_degree": 4, "min_girth": 5, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 17], [0, 18], [0, 19], [0, 20], [1, 14], [1, 15], [1, 16], [1, 20], [2, 12], [2, 13], [2, 16], [2, 19], [3, 11], [3, 13], [3, 15], [3, 18], [4, 10], [4, 13], [4, 14], [4, 17], [5, 9], [5, 12], [5, 15], [5, 17], [6, 9], [6, 10], [6, 11], [6, 20], [7, 8], [7, 11], [7, 16], [7, 17], [8, 10], [8, 12], [8, 18... | 1 |
construct-mc-pysms-girth-degree-l4-s0 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 4 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 27 vertices 0..26 such that:
- every vertex has degree between 3 and 5 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 27, "required_edges": [], "max_degree": 5, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 24], [0, 25], [0, 26], [1, 22], [1, 23], [1, 26], [2, 21], [2, 23], [2, 25], [3, 20], [3, 23], [3, 24], [4, 19], [4, 21], [4, 22], [5, 18], [5, 20], [5, 22], [5, 25], [6, 16], [6, 17], [6, 25], [7, 15], [7, 17], [7, 23], [8, 14], [8, 17], [8, 20], [9, 13], [9, 16], [9, 19], [10, 12], [10, 15], [10, 18], ... | 1 |
construct-mc-pysms-girth-degree-l4-s1 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 4 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 23 vertices 0..22 such that:
- every vertex has degree between 3 and 6 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 23, "required_edges": [], "max_degree": 6, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 20], [0, 21], [0, 22], [1, 18], [1, 19], [1, 22], [2, 17], [2, 19], [2, 21], [3, 15], [3, 16], [3, 22], [4, 14], [4, 16], [4, 21], [5, 13], [5, 16], [5, 19], [5, 20], [6, 13], [6, 15], [6, 17], [7, 13], [7, 14], [7, 18], [8, 12], [8, 15], [8, 18], [9, 11], [9, 14], [9, 17], [9, 22], [10, 11], [10, 13], [... | 1 |
construct-mc-pysms-girth-degree-l4-s2 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 4 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 23 vertices 0..22 such that:
- every vertex has degree between 3 and 4 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 23, "required_edges": [], "max_degree": 4, "min_degree": 3, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 20], [0, 21], [0, 22], [1, 18], [1, 19], [1, 22], [2, 17], [2, 19], [2, 21], [3, 17], [3, 18], [3, 20], [4, 16], [4, 19], [4, 20], [5, 15], [5, 18], [5, 21], [6, 14], [6, 17], [6, 22], [7, 13], [7, 16], [7, 22], [8, 12], [8, 13], [8, 17], [9, 11], [9, 13], [9, 14], [10, 11], [10, 12], [10, 16], [11, 21],... | 1 |
construct-mc-pysms-girth-degree-l5-s0 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 5 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- every vertex has degree between 3 and 4 (inclusive)
- the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 24, "required_edges": [], "max_degree": 4, "min_degree": 3, "min_girth": 7, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 21], [0, 22], [0, 23], [1, 19], [1, 20], [1, 23], [2, 17], [2, 18], [2, 23], [3, 15], [3, 16], [3, 22], [4, 14], [4, 16], [4, 20], [5, 13], [5, 16], [5, 18], [6, 12], [6, 15], [6, 19], [7, 11], [7, 14], [7, 17], [8, 10], [8, 12], [8, 18], [9, 10], [9, 11], [9, 22], [10, 20], [11, 13], [12, 21], [13, 19],... | 1 |
construct-mc-pysms-girth-degree-l5-s1 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 5 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 26 vertices 0..25 such that:
- every vertex has degree between 3 and 4 (inclusive)
- the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 26, "required_edges": [], "max_degree": 4, "min_degree": 3, "min_girth": 7, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 23], [0, 24], [0, 25], [1, 21], [1, 22], [1, 25], [2, 19], [2, 20], [2, 25], [3, 17], [3, 18], [3, 24], [4, 16], [4, 18], [4, 22], [5, 15], [5, 18], [5, 20], [6, 14], [6, 17], [6, 21], [7, 12], [7, 13], [7, 24], [8, 11], [8, 13], [8, 22], [9, 10], [9, 12], [9, 19], [10, 11], [10, 15], [11, 23], [12, 16],... | 1 |
construct-mc-pysms-girth-degree-l5-s2 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 5 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 28 vertices 0..27 such that:
- every vertex has degree between 4 and 7 (inclusive)
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 28, "required_edges": [], "max_degree": 7, "min_degree": 4, "min_girth": 6, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 24], [0, 25], [0, 26], [0, 27], [1, 21], [1, 22], [1, 23], [1, 27], [2, 19], [2, 20], [2, 23], [2, 26], [3, 18], [3, 20], [3, 22], [3, 25], [4, 17], [4, 20], [4, 21], [4, 24], [5, 16], [5, 19], [5, 22], [5, 24], [6, 16], [6, 17], [6, 18], [6, 27], [7, 15], [7, 18], [7, 23], [7, 24], [8, 15], [8, 17], [8,... | 1 |
construct-mc-pysms-girth-degree-l6-s0 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 6 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- every vertex has degree between 3 and 6 (inclusive)
- the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 24, "required_edges": [], "max_degree": 6, "min_degree": 3, "min_girth": 7, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 21], [0, 22], [0, 23], [1, 19], [1, 20], [1, 23], [2, 17], [2, 18], [2, 23], [3, 15], [3, 16], [3, 22], [4, 14], [4, 16], [4, 20], [5, 13], [5, 16], [5, 18], [6, 12], [6, 15], [6, 19], [7, 11], [7, 14], [7, 17], [8, 10], [8, 12], [8, 18], [9, 10], [9, 11], [9, 22], [10, 20], [11, 13], [12, 21], [13, 19],... | 1 |
construct-mc-pysms-girth-degree-l6-s1 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 6 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 26 vertices 0..25 such that:
- every vertex has degree between 3 and 6 (inclusive)
- the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 26, "required_edges": [], "max_degree": 6, "min_degree": 3, "min_girth": 7, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 23], [0, 24], [0, 25], [1, 21], [1, 22], [1, 25], [2, 19], [2, 20], [2, 25], [3, 17], [3, 18], [3, 24], [4, 16], [4, 18], [4, 22], [5, 15], [5, 18], [5, 20], [6, 14], [6, 17], [6, 21], [7, 14], [7, 16], [7, 23], [8, 13], [8, 17], [8, 19], [9, 13], [9, 15], [9, 23], [10, 12], [10, 16], [10, 19], [11, 12],... | 1 |
construct-mc-pysms-girth-degree-l6-s2 | construct | mc_pysms_girth_degree | graph_existence_girth_degree | graph_theory | competition | 6 | MathConstraint/pysms_girth_degree | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 26 vertices 0..25 such that:
- every vertex has degree between 3 and 5 (inclusive)
- the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vert... | {"vertices": 26, "required_edges": [], "max_degree": 5, "min_degree": 3, "min_girth": 7, "family": "mc_pysms_girth_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 23], [0, 24], [0, 25], [1, 21], [1, 22], [1, 25], [2, 19], [2, 20], [2, 25], [3, 17], [3, 18], [3, 24], [4, 16], [4, 18], [4, 22], [5, 15], [5, 18], [5, 20], [6, 14], [6, 17], [6, 21], [7, 14], [7, 16], [7, 23], [8, 13], [8, 17], [8, 19], [9, 13], [9, 15], [9, 23], [10, 12], [10, 16], [10, 19], [11, 12],... | 1 |
construct-mc-pysms-graph-builder-l1-s0 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 1 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- every vertex has degree between 2 and 3 (inclusive)
- the number of edges is between 9 and 18 (inclusive)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you... | {"vertices": 9, "required_edges": [[5, 6], [2, 3]], "max_degree": 3, "min_degree": 2, "max_chromatic_number": 4, "min_chromatic_number": 2, "min_edges": 9, "max_edges": 18, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [1, 5], [1, 6], [1, 8], [2, 3], [2, 4], [2, 8], [3, 4], [3, 7], [4, 6], [5, 6], [5, 7]], "coloring": [2, 0, 0, 1, 2, 1, 3, 0, 1]} | 1 |
construct-mc-pysms-graph-builder-l1-s1 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 1 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree between 1 and 2 (inclusive)
- the number of edges is between 9 and 11 (inclusive)
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours (y... | {"vertices": 12, "required_edges": [[5, 7], [4, 6]], "max_degree": 2, "min_degree": 1, "max_chromatic_number": 2, "min_chromatic_number": 2, "min_edges": 9, "max_edges": 11, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 11], [1, 9], [1, 10], [2, 8], [2, 10], [3, 7], [3, 9], [4, 6], [4, 8], [5, 6], [5, 7]], "coloring": [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-graph-builder-l2-s0 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 2 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- every vertex has degree between 2 and 3 (inclusive)
- the number of edges is between 12 and 17 (inclusive)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (yo... | {"vertices": 9, "required_edges": [[0, 8], [6, 7]], "max_degree": 3, "min_degree": 2, "max_chromatic_number": 4, "min_chromatic_number": 2, "min_edges": 12, "max_edges": 17, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8]], "coloring": [0, 0, 0, 1, 2, 3, 1, 2, 2]} | 1 |
construct-mc-pysms-graph-builder-l2-s1 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 2 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- every vertex has degree between 3 and 4 (inclusive)
- the number of edges is between 13 and 16 (inclusive)
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (yo... | {"vertices": 8, "required_edges": [[1, 7], [0, 7]], "max_degree": 4, "min_degree": 3, "max_chromatic_number": 3, "min_chromatic_number": 2, "min_edges": 13, "max_edges": 16, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 5], [0, 6], [0, 7], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]], "coloring": [0, 0, 0, 0, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-graph-builder-l3-s0 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 3 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- every vertex has degree between 2 and 2 (inclusive)
- the number of edges is between 9 and 14 (inclusive)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (y... | {"vertices": 13, "required_edges": [], "max_degree": 2, "min_degree": 2, "max_chromatic_number": 4, "min_chromatic_number": 2, "min_edges": 9, "max_edges": 14, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 11], [0, 12], [1, 10], [1, 12], [2, 8], [2, 9], [3, 7], [3, 9], [4, 5], [4, 6], [5, 6], [7, 8], [10, 11]], "coloring": [0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 1, 2, 1]} | 1 |
construct-mc-pysms-graph-builder-l3-s1 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 3 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree between 3 and 5 (inclusive)
- the number of edges is between 7 and 19 (inclusive)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (y... | {"vertices": 11, "required_edges": [[3, 7], [2, 9], [0, 9]], "max_degree": 5, "min_degree": 3, "max_chromatic_number": 4, "min_chromatic_number": 3, "min_edges": 7, "max_edges": 19, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [0, 9], [0, 10], [1, 8], [1, 9], [1, 10], [2, 7], [2, 8], [2, 9], [2, 10], [3, 6], [3, 7], [3, 10], [4, 5], [4, 6], [4, 10], [5, 6], [5, 9], [6, 7]], "coloring": [1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 0]} | 1 |
construct-mc-pysms-graph-builder-l4-s0 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 4 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree between 5 and 7 (inclusive)
- the number of edges is between 21 and 36 (inclusive)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (... | {"vertices": 14, "required_edges": [], "max_degree": 7, "min_degree": 5, "max_chromatic_number": 5, "min_chromatic_number": 3, "min_edges": 21, "max_edges": 36, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 8], [1, 10], [1, 11], [1, 12], [1, 13], [2, 6], [2, 7], [2, 9], [2, 12], [2, 13], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [4, 5], [4, 6], [4, 7], [4, 10], [4, 13], [5, 8], [5, 9], [5, 10], [6, 8], [6, 10], [6, 11], [6, 12], [7, 9], [7, 13], [8, 12], [11, 13]],... | 1 |
construct-mc-pysms-graph-builder-l4-s1 | construct | mc_pysms_graph_builder | graph_existence_graph_builder | graph_theory | competition | 4 | MathConstraint/pysms_graph_builder | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree between 4 and 6 (inclusive)
- the number of edges is between 21 and 37 (inclusive)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (... | {"vertices": 14, "required_edges": [], "max_degree": 6, "min_degree": 4, "max_chromatic_number": 4, "min_chromatic_number": 3, "min_edges": 21, "max_edges": 37, "family": "mc_pysms_graph_builder", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [0, 11], [0, 12], [0, 13], [1, 6], [1, 7], [1, 8], [1, 9], [1, 13], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 13], [4, 5], [4, 8], [4, 9], [5, 6], [5, 9], [5, 12], [6, 7], [6, 8], [6, 12], [7, 12], [7, 13], [8, 11], [10, 11], [10, 12], [10, 13], [11, 12], [1... | 1 |
construct-mc-pysms-independent-connectivity-l1-s0 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 1 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the graph contains no independent set of size 5 (maximum independent set size at most 4)
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where ... | {"vertices": 9, "required_edges": [], "max_independent_set": 4, "min_connectivity": 1, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-independent-connectivity-l1-s1 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 1 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- the graph contains no independent set of size 3 (maximum independent set size at most 2)
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where ... | {"vertices": 8, "required_edges": [], "max_independent_set": 2, "min_connectivity": 1, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]]} | 1 |
construct-mc-pysms-independent-connectivity-l1-s2 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 1 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the graph contains no independent set of size 3 (maximum independent set size at most 2)
- the vertex-connectivity is at least 2: deleting any set of fewer than 2 vertices leaves a connected graph
- it contains each of the following edges: (3... | {"vertices": 9, "required_edges": [[3, 6], [1, 4], [0, 2], [3, 8], [1, 3], [7, 8], [5, 6]], "max_independent_set": 2, "min_connectivity": 2, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-independent-connectivity-l2-s0 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 2 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the graph contains no independent set of size 4 (maximum independent set size at most 3)
- the vertex-connectivity is at least 2: deleting any set of fewer than 2 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where... | {"vertices": 10, "required_edges": [], "max_independent_set": 3, "min_connectivity": 2, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 9... | 1 |
construct-mc-pysms-independent-connectivity-l2-s1 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 2 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the graph contains no independent set of size 7 (maximum independent set size at most 6)
- the vertex-connectivity is at least 2: deleting any set of fewer than 2 vertices leaves a connected graph
- it contains each of the following edges: (... | {"vertices": 10, "required_edges": [[0, 3], [3, 8], [2, 9], [0, 5], [0, 4], [1, 7], [1, 4], [1, 6], [4, 8]], "max_independent_set": 6, "min_connectivity": 2, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 9... | 1 |
construct-mc-pysms-independent-connectivity-l2-s2 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 2 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the graph contains no independent set of size 6 (maximum independent set size at most 5)
- the vertex-connectivity is at least 2: deleting any set of fewer than 2 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} wher... | {"vertices": 11, "required_edges": [], "max_independent_set": 5, "min_connectivity": 2, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 8], [... | 1 |
construct-mc-pysms-independent-connectivity-l3-s0 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 3 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- the graph contains no independent set of size 6 (maximum independent set size at most 5)
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
- it contains each of the following edges: ... | {"vertices": 16, "required_edges": [[6, 14], [13, 14], [0, 12], [2, 11], [2, 10], [8, 14], [7, 14], [6, 15], [5, 13], [12, 15], [2, 14], [0, 11], [0, 8], [8, 15], [14, 15], [4, 5], [5, 7], [2, 13], [0, 2], [0, 1], [0, 10], [0, 5], [10, 11], [3, 7]], "max_independent_set": 5, "min_connectivity": 1, "family": "mc_pysms_i... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], ... | 1 |
construct-mc-pysms-independent-connectivity-l3-s1 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 3 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the graph contains no independent set of size 5 (maximum independent set size at most 4)
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where ... | {"vertices": 9, "required_edges": [], "max_independent_set": 4, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-independent-connectivity-l3-s2 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 3 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the graph contains no independent set of size 5 (maximum independent set size at most 4)
- the vertex-connectivity is at least 3: deleting any set of fewer than 3 vertices leaves a connected graph
- it contains each of the following edges: ... | {"vertices": 11, "required_edges": [[0, 6], [1, 10], [3, 6], [3, 8], [2, 7], [0, 4], [1, 6], [0, 8], [1, 2], [5, 10], [0, 3]], "max_independent_set": 4, "min_connectivity": 3, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 8], [... | 1 |
construct-mc-pysms-independent-connectivity-l4-s0 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 4 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- the graph contains no independent set of size 4 (maximum independent set size at most 3)
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} wher... | {"vertices": 12, "required_edges": [], "max_independent_set": 3, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11... | 1 |
construct-mc-pysms-independent-connectivity-l4-s1 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 4 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the graph contains no independent set of size 5 (maximum independent set size at most 4)
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
- it contains each of the following edges: ... | {"vertices": 15, "required_edges": [[2, 5], [8, 11], [0, 2], [5, 9], [2, 10], [2, 11], [4, 13], [7, 14], [2, 13], [11, 14], [4, 6], [9, 10], [4, 14], [12, 13], [3, 4], [0, 7], [1, 5], [2, 3], [5, 8], [11, 12], [7, 10]], "max_independent_set": 4, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "sub... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], ... | 1 |
construct-mc-pysms-independent-connectivity-l4-s2 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 4 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the graph contains no independent set of size 5 (maximum independent set size at most 4)
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
- it contains each of the following edges: ... | {"vertices": 11, "required_edges": [[5, 9], [2, 7], [1, 4], [0, 8], [1, 5], [1, 9], [6, 8], [5, 6], [4, 8], [7, 8], [3, 8]], "max_independent_set": 4, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 8], [... | 1 |
construct-mc-pysms-independent-connectivity-l5-s0 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 5 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 20 vertices 0..19 such that:
- the graph contains no independent set of size 4 (maximum independent set size at most 3)
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} wher... | {"vertices": 20, "required_edges": [], "max_independent_set": 3, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1... | 1 |
construct-mc-pysms-independent-connectivity-l5-s1 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 5 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 21 vertices 0..20 such that:
- the graph contains no independent set of size 5 (maximum independent set size at most 4)
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} wher... | {"vertices": 21, "required_edges": [], "max_independent_set": 4, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1... | 1 |
construct-mc-pysms-independent-connectivity-l5-s2 | construct | mc_pysms_independent_connectivity | graph_existence_independent_connectivity | graph_theory | competition | 5 | MathConstraint/pysms_independent_connectivity | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- the graph contains no independent set of size 6 (maximum independent set size at most 5)
- the vertex-connectivity is at least 5: deleting any set of fewer than 5 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} wher... | {"vertices": 16, "required_edges": [], "max_independent_set": 5, "min_connectivity": 5, "family": "mc_pysms_independent_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], ... | 1 |
construct-mc-pysms-min-connectivity-l1-s0 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 1 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..7, listed once
Write your final answer as JSO... | {"vertices": 8, "required_edges": [], "min_connectivity": 1, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]]} | 1 |
construct-mc-pysms-min-connectivity-l1-s1 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 1 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
- it contains each of the following edges: (2,6), (5,7), (2,5), (1,2), (4,6), (3,6), (1,5)
Answer format: {"edges": [[u, v], ...]} where ... | {"vertices": 9, "required_edges": [[2, 6], [5, 7], [2, 5], [1, 2], [4, 6], [3, 6], [1, 5]], "min_connectivity": 1, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-min-connectivity-l2-s0 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 2 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, listed once
Write your final answer as ... | {"vertices": 14, "required_edges": [], "min_connectivity": 1, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [3, 4], [... | 1 |
construct-mc-pysms-min-connectivity-l2-s1 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 2 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..14, listed once
Write your final answer as ... | {"vertices": 15, "required_edges": [], "min_connectivity": 1, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], ... | 1 |
construct-mc-pysms-min-connectivity-l3-s0 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 3 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed once
Write your final answer as ... | {"vertices": 11, "required_edges": [], "min_connectivity": 4, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 8], [... | 1 |
construct-mc-pysms-min-connectivity-l3-s1 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 3 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- the vertex-connectivity is at least 2: deleting any set of fewer than 2 vertices leaves a connected graph
- it contains each of the following edges: (5,13), (8,15), (1,4), (0,4), (8,10), (0,15), (3,10), (7,12), (10,15), (3,7), (4,5), (2,9), (... | {"vertices": 16, "required_edges": [[5, 13], [8, 15], [1, 4], [0, 4], [8, 10], [0, 15], [3, 10], [7, 12], [10, 15], [3, 7], [4, 5], [2, 9], [0, 9], [3, 15], [0, 10], [6, 9], [3, 5], [3, 4], [1, 14], [6, 8], [10, 11], [3, 14], [4, 6], [7, 9]], "min_connectivity": 2, "family": "mc_pysms_min_connectivity", "subset": "cons... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], ... | 1 |
construct-mc-pysms-min-connectivity-l3-s2 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 3 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 18 vertices 0..17 such that:
- the vertex-connectivity is at least 2: deleting any set of fewer than 2 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..17, listed once
Write your final answer as ... | {"vertices": 18, "required_edges": [], "min_connectivity": 2, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6... | 1 |
construct-mc-pysms-min-connectivity-l4-s0 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 4 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the vertex-connectivity is at least 3: deleting any set of fewer than 3 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..14, listed once
Write your final answer as ... | {"vertices": 15, "required_edges": [], "min_connectivity": 3, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], ... | 1 |
construct-mc-pysms-min-connectivity-l4-s1 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 4 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the vertex-connectivity is at least 3: deleting any set of fewer than 3 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, listed once
Write your final answer as ... | {"vertices": 14, "required_edges": [], "min_connectivity": 3, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [3, 4], [... | 1 |
construct-mc-pysms-min-connectivity-l5-s0 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 5 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 18 vertices 0..17 such that:
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
- it contains each of the following edges: (2,9), (0,10), (15,17), (12,15), (2,6), (3,17), (0,14), (11,13), (9,14), (6,12), (10,13), (1,... | {"vertices": 18, "required_edges": [[2, 9], [0, 10], [15, 17], [12, 15], [2, 6], [3, 17], [0, 14], [11, 13], [9, 14], [6, 12], [10, 13], [1, 10], [11, 17], [10, 16], [1, 5], [6, 14], [5, 10], [1, 9], [4, 14], [15, 16], [3, 12], [13, 16], [2, 3], [10, 15], [7, 13], [6, 16], [2, 8], [3, 10], [0, 15], [2, 16]], "min_conne... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6... | 1 |
construct-mc-pysms-min-connectivity-l5-s1 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 5 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- the vertex-connectivity is at least 5: deleting any set of fewer than 5 vertices leaves a connected graph
- it contains each of the following edges: (1,10), (4,10), (7,10), (1,6), (5,13), (3,6), (0,6), (0,15), (9,13), (3,12), (2,7), (4,14), (... | {"vertices": 16, "required_edges": [[1, 10], [4, 10], [7, 10], [1, 6], [5, 13], [3, 6], [0, 6], [0, 15], [9, 13], [3, 12], [2, 7], [4, 14], [1, 12], [8, 13], [11, 14], [5, 12], [4, 12], [5, 14], [0, 4], [6, 7], [8, 9], [9, 12], [2, 8], [10, 14]], "min_connectivity": 5, "family": "mc_pysms_min_connectivity", "subset": "... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], ... | 1 |
construct-mc-pysms-min-connectivity-l5-s2 | construct | mc_pysms_min_connectivity | graph_existence_min_connectivity | graph_theory | competition | 5 | MathConstraint/pysms_min_connectivity | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 17 vertices 0..16 such that:
- the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..16, listed once
Write your final answer as ... | {"vertices": 17, "required_edges": [], "min_connectivity": 4, "family": "mc_pysms_min_connectivity", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8],... | 1 |
construct-mc-pysms-min-degree-l1-s0 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 1 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- every vertex has degree at least 4
- it contains each of the following edges: (1,5), (0,1), (1,3), (3,6), (2,8), (4,5), (4,6)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..8, listed once
Write yo... | {"vertices": 9, "required_edges": [[1, 5], [0, 1], [1, 3], [3, 6], [2, 8], [4, 5], [4, 6]], "min_degree": 4, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-min-degree-l1-s1 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 1 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- every vertex has degree at least 3
- it contains each of the following edges: (2,6), (0,6), (4,7), (6,7), (3,7)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..7, listed once
Write your final answe... | {"vertices": 8, "required_edges": [[2, 6], [0, 6], [4, 7], [6, 7], [3, 7]], "min_degree": 3, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]]} | 1 |
construct-mc-pysms-min-degree-l2-s0 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 2 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- every vertex has degree at least 5
- it contains each of the following edges: (5,7), (1,5), (3,6), (5,6), (4,5), (4,6), (0,7)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..8, listed once
Write yo... | {"vertices": 9, "required_edges": [[5, 7], [1, 5], [3, 6], [5, 6], [4, 5], [4, 6], [0, 7]], "min_degree": 5, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-min-degree-l2-s1 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 2 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- every vertex has degree at least 6
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/in... | {"vertices": 10, "required_edges": [], "min_degree": 6, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 9... | 1 |
construct-mc-pysms-min-degree-l3-s0 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 3 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree at least 3
- it contains each of the following edges: (7,9), (1,3), (0,8), (6,11), (1,6), (3,11), (4,9), (4,11), (6,8), (10,11), (5,11), (1,10), (2,6)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair ... | {"vertices": 12, "required_edges": [[7, 9], [1, 3], [0, 8], [6, 11], [1, 6], [3, 11], [4, 9], [4, 11], [6, 8], [10, 11], [5, 11], [1, 10], [2, 6]], "min_degree": 3, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11... | 1 |
construct-mc-pysms-min-degree-l3-s1 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 3 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- every vertex has degree at least 4
- it contains each of the following edges: (8,9), (2,8), (2,7), (2,9), (0,1), (0,8), (1,8), (3,8), (5,8)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed... | {"vertices": 10, "required_edges": [[8, 9], [2, 8], [2, 7], [2, 9], [0, 1], [0, 8], [1, 8], [3, 8], [5, 8]], "min_degree": 4, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 9... | 1 |
construct-mc-pysms-min-degree-l3-s2 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 3 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree at least 3
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"vertices": 11, "required_edges": [], "min_degree": 3, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 8], [... | 1 |
construct-mc-pysms-min-degree-l4-s0 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 4 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- every vertex has degree at least 6
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..12, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"vertices": 13, "required_edges": [], "min_degree": 6, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [3, 4], [3, 5], [3, 6], [3, 7], [3, ... | 1 |
construct-mc-pysms-min-degree-l4-s1 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 4 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- every vertex has degree at least 5
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..12, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"vertices": 13, "required_edges": [], "min_degree": 5, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [3, 4], [3, 5], [3, 6], [3, 7], [3, ... | 1 |
construct-mc-pysms-min-degree-l5-s0 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 5 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 18 vertices 0..17 such that:
- every vertex has degree at least 5
- it contains each of the following edges: (3,15), (11,13), (13,17), (2,11), (11,17), (2,12), (7,17), (9,17), (3,5), (0,16), (1,14), (7,9), (0,9), (6,11), (3,11), (0,2), (1,17), (4,8), (5,15), (1,15), (2,15)... | {"vertices": 18, "required_edges": [[3, 15], [11, 13], [13, 17], [2, 11], [11, 17], [2, 12], [7, 17], [9, 17], [3, 5], [0, 16], [1, 14], [7, 9], [0, 9], [6, 11], [3, 11], [0, 2], [1, 17], [4, 8], [5, 15], [1, 15], [2, 15], [15, 17], [4, 16], [0, 8], [4, 6], [8, 13], [13, 14], [2, 10], [6, 13], [9, 12]], "min_degree": 5... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6... | 1 |
construct-mc-pysms-min-degree-l5-s1 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 5 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree at least 6
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..14, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"vertices": 15, "required_edges": [], "min_degree": 6, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], ... | 1 |
construct-mc-pysms-min-degree-l5-s2 | construct | mc_pysms_min_degree | graph_existence_min_degree | graph_theory | competition | 5 | MathConstraint/pysms_min_degree | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- every vertex has degree at least 1
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..15, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"vertices": 16, "required_edges": [], "min_degree": 1, "family": "mc_pysms_min_degree", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], ... | 1 |
construct-mc-pysms-min-girth-l1-s0 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 1 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..7, listed once
Write your final answer as JSON... | {"vertices": 8, "required_edges": [], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7]]} | 1 |
construct-mc-pysms-min-girth-l1-s1 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 1 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the girth is at least 8: the graph has no cycle of length less than 8 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..8, listed once
Write your final answer as JSON... | {"vertices": 9, "required_edges": [], "min_girth": 8, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-min-girth-l2-s0 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 2 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the girth is at least 3: the graph has no cycle of length less than 3 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..8, listed once
Write your final answer as JSON... | {"vertices": 9, "required_edges": [], "min_girth": 3, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]} | 1 |
construct-mc-pysms-min-girth-l2-s1 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 2 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the girth is at least 3: the graph has no cycle of length less than 3 (a graph without cycles qualifies)
- it contains each of the following edges: (0,7), (0,4), (0,2), (2,9), (1,4), (4,6), (2,8), (1,8), (3,9)
Answer format: {"edges": [[u, v]... | {"vertices": 10, "required_edges": [[0, 7], [0, 4], [0, 2], [2, 9], [1, 4], [4, 6], [2, 8], [1, 8], [3, 9]], "min_girth": 3, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 9... | 1 |
construct-mc-pysms-min-girth-l2-s2 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 2 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the girth is at least 4: the graph has no cycle of length less than 4 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed once
Write your final answer as JSO... | {"vertices": 10, "required_edges": [], "min_girth": 4, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9]]} | 1 |
construct-mc-pysms-min-girth-l3-s0 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 3 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed once
Write your final answer as J... | {"vertices": 11, "required_edges": [], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [8, 10], [9, 10]]} | 1 |
construct-mc-pysms-min-girth-l3-s1 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 3 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- the girth is at least 3: the graph has no cycle of length less than 3 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..11, listed once
Write your final answer as J... | {"vertices": 12, "required_edges": [], "min_girth": 3, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11... | 1 |
construct-mc-pysms-min-girth-l4-s0 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 4 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
- it contains each of the following edges: (9,13), (4,13)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct ... | {"vertices": 14, "required_edges": [[9, 13], [4, 13]], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 13], [1, 13], [2, 13], [3, 13], [4, 13], [5, 13], [6, 13], [7, 13], [8, 13], [9, 13], [10, 13], [11, 13], [12, 13]]} | 1 |
construct-mc-pysms-min-girth-l4-s1 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 4 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 17 vertices 0..16 such that:
- the girth is at least 3: the graph has no cycle of length less than 3 (a graph without cycles qualifies)
- it contains each of the following edges: (1,16), (5,15), (4,13), (2,7), (6,13), (8,9), (2,6), (8,15), (5,6), (7,15), (2,5), (3,12), (1,... | {"vertices": 17, "required_edges": [[1, 16], [5, 15], [4, 13], [2, 7], [6, 13], [8, 9], [2, 6], [8, 15], [5, 6], [7, 15], [2, 5], [3, 12], [1, 11], [9, 14], [4, 7], [12, 16], [4, 16], [1, 9], [7, 11], [6, 11], [13, 14], [3, 16], [10, 12], [12, 13], [0, 12], [1, 3], [0, 14]], "min_girth": 3, "family": "mc_pysms_min_girt... | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8],... | 1 |
construct-mc-pysms-min-girth-l4-s2 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 4 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 17 vertices 0..16 such that:
- the girth is at least 4: the graph has no cycle of length less than 4 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..16, listed once
Write your final answer as J... | {"vertices": 17, "required_edges": [], "min_girth": 4, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 16], [1, 16], [2, 16], [3, 16], [4, 16], [5, 16], [6, 16], [7, 16], [8, 16], [9, 16], [10, 16], [11, 16], [12, 16], [13, 16], [14, 16], [15, 16]]} | 1 |
construct-mc-pysms-min-girth-l5-s0 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 5 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the girth is at least 8: the graph has no cycle of length less than 8 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, listed once
Write your final answer as J... | {"vertices": 14, "required_edges": [], "min_girth": 8, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 13], [1, 13], [2, 13], [3, 13], [4, 13], [5, 13], [6, 13], [7, 13], [8, 13], [9, 13], [10, 13], [11, 13], [12, 13]]} | 1 |
construct-mc-pysms-min-girth-l5-s1 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 5 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- the girth is at least 8: the graph has no cycle of length less than 8 (a graph without cycles qualifies)
- it contains each of the following edges: (11,15), (3,15), (5,15)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of ... | {"vertices": 16, "required_edges": [[11, 15], [3, 15], [5, 15]], "min_girth": 8, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 15], [1, 15], [2, 15], [3, 15], [4, 15], [5, 15], [6, 15], [7, 15], [8, 15], [9, 15], [10, 15], [11, 15], [12, 15], [13, 15], [14, 15]]} | 1 |
construct-mc-pysms-min-girth-l5-s2 | construct | mc_pysms_min_girth | graph_existence_min_girth | graph_theory | competition | 5 | MathConstraint/pysms_min_girth | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..23, listed once
Write your final answer as J... | {"vertices": 24, "required_edges": [], "min_girth": 7, "family": "mc_pysms_min_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 23], [1, 23], [2, 23], [3, 23], [4, 23], [5, 23], [6, 23], [7, 23], [8, 23], [9, 23], [10, 23], [11, 23], [12, 23], [13, 23], [14, 23], [15, 23], [16, 23], [17, 23], [18, 23], [19, 23], [20, 23], [21, 23], [22, 23]]} | 1 |
construct-mc-pysms-mtf-l1-s0 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 1 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 7 vertices 0..6 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (0,6), (1,5)
Answer format: {"edges"... | {"vertices": 7, "required_edges": [[0, 6], [1, 5]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 5], [0, 6], [1, 5], [1, 6], [2, 5], [2, 6], [3, 5], [3, 6], [4, 5], [4, 6]]} | 1 |
construct-mc-pysms-mtf-l1-s1 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 1 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 6 vertices 0..5 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (3,5)
Answer format: {"edges": [[u, ... | {"vertices": 6, "required_edges": [[3, 5]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [1, 4], [1, 5], [2, 4], [2, 5], [3, 4], [3, 5]]} | 1 |
construct-mc-pysms-mtf-l2-s0 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 2 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (0,6), (2,6)
Answer format: {"edges"... | {"vertices": 8, "required_edges": [[0, 6], [2, 6]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 6], [0, 7], [1, 6], [1, 7], [2, 6], [2, 7], [3, 6], [3, 7], [4, 6], [4, 7], [5, 6], [5, 7]]} | 1 |
construct-mc-pysms-mtf-l2-s1 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 2 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (4,7), (0,7)
Answer format: {"edges"... | {"vertices": 9, "required_edges": [[4, 7], [0, 7]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [1, 7], [1, 8], [2, 7], [2, 8], [3, 7], [3, 8], [4, 7], [4, 8], [5, 7], [5, 8], [6, 7], [6, 8]]} | 1 |
construct-mc-pysms-mtf-l3-s0 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 3 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct v... | {"vertices": 13, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 11], [0, 12], [1, 11], [1, 12], [2, 11], [2, 12], [3, 11], [3, 12], [4, 11], [4, 12], [5, 11], [5, 12], [6, 11], [6, 12], [7, 11], [7, 12], [8, 11], [8, 12], [9, 11], [9, 12], [10, 11], [10, 12]]} | 1 |
construct-mc-pysms-mtf-l3-s1 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 3 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct v... | {"vertices": 12, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 10], [0, 11], [1, 10], [1, 11], [2, 10], [2, 11], [3, 10], [3, 11], [4, 10], [4, 11], [5, 10], [5, 11], [6, 10], [6, 11], [7, 10], [7, 11], [8, 10], [8, 11], [9, 10], [9, 11]]} | 1 |
construct-mc-pysms-mtf-l3-s2 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 3 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct ve... | {"vertices": 10, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [0, 9], [1, 8], [1, 9], [2, 8], [2, 9], [3, 8], [3, 9], [4, 8], [4, 9], [5, 8], [5, 9], [6, 8], [6, 9], [7, 8], [7, 9]]} | 1 |
construct-mc-pysms-mtf-l4-s0 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 4 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (2,14), (6,13), (7,13), (10,13), (6... | {"vertices": 15, "required_edges": [[2, 14], [6, 13], [7, 13], [10, 13], [6, 14]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 13], [0, 14], [1, 13], [1, 14], [2, 13], [2, 14], [3, 13], [3, 14], [4, 13], [4, 14], [5, 13], [5, 14], [6, 13], [6, 14], [7, 13], [7, 14], [8, 13], [8, 14], [9, 13], [9, 14], [10, 13], [10, 14], [11, 13], [11, 14], [12, 13], [12, 14]]} | 1 |
construct-mc-pysms-mtf-l4-s1 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 4 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct v... | {"vertices": 14, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 12], [0, 13], [1, 12], [1, 13], [2, 12], [2, 13], [3, 12], [3, 13], [4, 12], [4, 13], [5, 12], [5, 13], [6, 12], [6, 13], [7, 12], [7, 13], [8, 12], [8, 13], [9, 12], [9, 13], [10, 12], [10, 13], [11, 12], [11, 13]]} | 1 |
construct-mc-pysms-mtf-l5-s0 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 5 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 20 vertices 0..19 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (1,18), (4,18), (16,18), (4,19), (1... | {"vertices": 20, "required_edges": [[1, 18], [4, 18], [16, 18], [4, 19], [17, 18], [11, 19], [3, 19]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 18], [0, 19], [1, 18], [1, 19], [2, 18], [2, 19], [3, 18], [3, 19], [4, 18], [4, 19], [5, 18], [5, 19], [6, 18], [6, 19], [7, 18], [7, 19], [8, 18], [8, 19], [9, 18], [9, 19], [10, 18], [10, 19], [11, 18], [11, 19], [12, 18], [12, 19], [13, 18], [13, 19], [14, 18], [14, 19], [15, 18], [15, 19], [16, 18],... | 1 |
construct-mc-pysms-mtf-l5-s1 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 5 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 17 vertices 0..16 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
- it contains each of the following edges: (0,15), (3,15), (6,15), (9,15), (11... | {"vertices": 17, "required_edges": [[0, 15], [3, 15], [6, 15], [9, 15], [11, 15], [14, 16]], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 15], [0, 16], [1, 15], [1, 16], [2, 15], [2, 16], [3, 15], [3, 16], [4, 15], [4, 16], [5, 15], [5, 16], [6, 15], [6, 16], [7, 15], [7, 16], [8, 15], [8, 16], [9, 15], [9, 16], [10, 15], [10, 16], [11, 15], [11, 16], [12, 15], [12, 16], [13, 15], [13, 16], [14, 15], [14, 16]]} | 1 |
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