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-nppc-3col-l4-s6 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 4 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 2], [0, 8], [0, 19], [0, 20], [0, 23], [0, 27], [1, 2], [1, 8], [1, 16], [1, 24], [2, 14], [2, 18], [2, 19], [2, 22], [3, 5], [3, 6], [3, 9], [3, 13], [3, 15], [3, 21], [3, 26], [4, 9], [4, 10], [4, 17], [4, 29], [5, 14], [5, 16], [5, 24], [6, 13], [6, 18... | {"num_nodes": 30, "edges": [[0, 1], [0, 2], [0, 8], [0, 19], [0, 20], [0, 23], [0, 27], [1, 2], [1, 8], [1, 16], [1, 24], [2, 14], [2, 18], [2, 19], [2, 22], [3, 5], [3, 6], [3, 9], [3, 13], [3, 15], [3, 21], [3, 26], [4, 9], [4, 10], [4, 17], [4, 29], [5, 14], [5, 16], [5, 24], [6, 13], [6, 18], [6, 19], [6, 23], [6, ... | null | null | null | {"coloring": [0, 2, 1, 2, 0, 1, 0, 2, 1, 1, 2, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 0, 1, 1, 2]} | 1 |
construct-nppc-3col-l4-s7 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 4 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 30 vertices labelled 0..29 and edge list
[[0, 8], [0, 11], [0, 13], [0, 14], [0, 18], [0, 28], [1, 3], [1, 5], [1, 9], [1, 16], [1, 18], [1, 22], [1, 28], [2, 4], [2, 20], [2, 26], [2, 29], [3, 13], [3, 14], [3, 15], [3, 19], [3, 24], [3, 28], [4, 26], [5, 11], [5, 14], [5, 15], [5, 24], [6, 9], [6, 11], [6,... | {"num_nodes": 30, "edges": [[0, 8], [0, 11], [0, 13], [0, 14], [0, 18], [0, 28], [1, 3], [1, 5], [1, 9], [1, 16], [1, 18], [1, 22], [1, 28], [2, 4], [2, 20], [2, 26], [2, 29], [3, 13], [3, 14], [3, 15], [3, 19], [3, 24], [3, 28], [4, 26], [5, 11], [5, 14], [5, 15], [5, 24], [6, 9], [6, 11], [6, 14], [6, 15], [6, 18], [... | null | null | null | {"coloring": [1, 2, 1, 1, 0, 1, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 2, 1, 2, 1, 0, 2]} | 1 |
construct-nppc-3col-l4-s8 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 4 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 30 vertices labelled 0..29 and edge list
[[0, 4], [0, 10], [0, 11], [0, 15], [0, 25], [0, 27], [0, 28], [0, 29], [1, 6], [1, 9], [1, 12], [1, 14], [1, 18], [2, 26], [3, 8], [3, 11], [3, 12], [3, 13], [3, 20], [3, 21], [4, 6], [4, 7], [4, 16], [4, 29], [5, 7], [5, 12], [5, 20], [5, 23], [6, 9], [6, 11], [6, 1... | {"num_nodes": 30, "edges": [[0, 4], [0, 10], [0, 11], [0, 15], [0, 25], [0, 27], [0, 28], [0, 29], [1, 6], [1, 9], [1, 12], [1, 14], [1, 18], [2, 26], [3, 8], [3, 11], [3, 12], [3, 13], [3, 20], [3, 21], [4, 6], [4, 7], [4, 16], [4, 29], [5, 7], [5, 12], [5, 20], [5, 23], [6, 9], [6, 11], [6, 14], [6, 15], [6, 16], [6,... | null | null | null | {"coloring": [1, 2, 1, 1, 2, 2, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0]} | 1 |
construct-nppc-3col-l4-s9 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 4 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 30 vertices labelled 0..29 and edge list
[[0, 3], [0, 10], [0, 20], [1, 4], [1, 7], [1, 8], [1, 10], [1, 14], [1, 21], [2, 10], [2, 14], [2, 17], [2, 21], [2, 25], [2, 29], [3, 8], [3, 12], [3, 14], [3, 25], [4, 6], [4, 13], [4, 20], [4, 22], [4, 27], [5, 8], [5, 20], [6, 8], [6, 10], [6, 17], [6, 18], [7, 9... | {"num_nodes": 30, "edges": [[0, 3], [0, 10], [0, 20], [1, 4], [1, 7], [1, 8], [1, 10], [1, 14], [1, 21], [2, 10], [2, 14], [2, 17], [2, 21], [2, 25], [2, 29], [3, 8], [3, 12], [3, 14], [3, 25], [4, 6], [4, 13], [4, 20], [4, 22], [4, 27], [5, 8], [5, 20], [6, 8], [6, 10], [6, 17], [6, 18], [7, 9], [7, 11], [7, 27], [7, ... | null | null | null | {"coloring": [2, 1, 2, 1, 2, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0]} | 1 |
construct-nppc-3col-l5-s0 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 3], [0, 10], [0, 24], [0, 30], [0, 39], [0, 41], [0, 44], [0, 48], [1, 7], [1, 21], [1, 22], [1, 33], [1, 34], [1, 39], [2, 12], [2, 43], [2, 49], [3, 13], [3, 48], [3, 55], [3, 57], [4, 5], [4, 7], [4, 20], [4, 21], [4, 32], [4, 42], [4, 52], [5, 15], [5, 18], [... | {"num_nodes": 60, "edges": [[0, 3], [0, 10], [0, 24], [0, 30], [0, 39], [0, 41], [0, 44], [0, 48], [1, 7], [1, 21], [1, 22], [1, 33], [1, 34], [1, 39], [2, 12], [2, 43], [2, 49], [3, 13], [3, 48], [3, 55], [3, 57], [4, 5], [4, 7], [4, 20], [4, 21], [4, 32], [4, 42], [4, 52], [5, 15], [5, 18], [5, 19], [5, 29], [5, 33],... | null | null | null | {"coloring": [1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 0, 1, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1]} | 1 |
construct-nppc-3col-l5-s1 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 23], [0, 29], [0, 33], [0, 54], [0, 56], [1, 2], [1, 25], [1, 32], [1, 46], [1, 54], [1, 55], [1, 58], [2, 8], [2, 10], [2, 12], [2, 21], [2, 40], [2, 46], [2, 59], [3, 7], [3, 10], [3, 19], [3, 20], [3, 23], [3, 52], [4, 6], [4, 19], [4, 26], [4, 47], [5, 7], [5... | {"num_nodes": 60, "edges": [[0, 23], [0, 29], [0, 33], [0, 54], [0, 56], [1, 2], [1, 25], [1, 32], [1, 46], [1, 54], [1, 55], [1, 58], [2, 8], [2, 10], [2, 12], [2, 21], [2, 40], [2, 46], [2, 59], [3, 7], [3, 10], [3, 19], [3, 20], [3, 23], [3, 52], [4, 6], [4, 19], [4, 26], [4, 47], [5, 7], [5, 11], [5, 20], [5, 21], ... | null | null | null | {"coloring": [2, 0, 2, 1, 1, 2, 2, 0, 1, 2, 0, 0, 0, 2, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 1, 0, 2, 2, 0, 1, 0, 0, 1, 2, 1, 1, 2, 2, 0, 2, 2, 1, 0, 1, 1, 1, 1, 0, 2, 1, 2, 0, 2, 2, 1]} | 1 |
construct-nppc-3col-l5-s2 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 4], [0, 44], [0, 58], [1, 3], [1, 6], [1, 9], [1, 26], [1, 55], [2, 11], [2, 29], [2, 37], [2, 47], [2, 50], [2, 55], [3, 28], [3, 41], [3, 42], [3, 47], [3, 50], [3, 53], [4, 7], [4, 19], [4, 20], [4, 25], [4, 26], [4, 31], [4, 56], [5, 9], [5, 13], [5, 26], [5,... | {"num_nodes": 60, "edges": [[0, 4], [0, 44], [0, 58], [1, 3], [1, 6], [1, 9], [1, 26], [1, 55], [2, 11], [2, 29], [2, 37], [2, 47], [2, 50], [2, 55], [3, 28], [3, 41], [3, 42], [3, 47], [3, 50], [3, 53], [4, 7], [4, 19], [4, 20], [4, 25], [4, 26], [4, 31], [4, 56], [5, 9], [5, 13], [5, 26], [5, 34], [5, 37], [5, 57], [... | null | null | null | {"coloring": [1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 0, 1, 1, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 1, 2, 1, 0, 0]} | 1 |
construct-nppc-3col-l5-s3 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 7], [0, 10], [0, 18], [0, 36], [0, 37], [0, 41], [0, 43], [1, 2], [1, 10], [1, 13], [1, 17], [1, 18], [1, 21], [1, 30], [1, 31], [1, 35], [1, 43], [2, 17], [2, 37], [2, 58], [3, 6], [3, 11], [3, 16], [3, 21], [3, 28], [3, 39], [3, 43], [3, 45], [3, 47], [3, 52], ... | {"num_nodes": 60, "edges": [[0, 7], [0, 10], [0, 18], [0, 36], [0, 37], [0, 41], [0, 43], [1, 2], [1, 10], [1, 13], [1, 17], [1, 18], [1, 21], [1, 30], [1, 31], [1, 35], [1, 43], [2, 17], [2, 37], [2, 58], [3, 6], [3, 11], [3, 16], [3, 21], [3, 28], [3, 39], [3, 43], [3, 45], [3, 47], [3, 52], [3, 59], [4, 7], [4, 24],... | null | null | null | {"coloring": [1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 1, 0, 2, 1, 1, 1, 2, 2, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0, 1, 2, 2, 2, 0, 1, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2]} | 1 |
construct-nppc-3col-l5-s4 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 9], [0, 19], [0, 40], [0, 57], [1, 4], [1, 18], [1, 20], [1, 37], [1, 43], [1, 46], [1, 50], [1, 51], [2, 17], [2, 25], [2, 40], [2, 54], [3, 9], [3, 17], [3, 25], [3, 27], [3, 55], [4, 14], [4, 16], [4, 29], [4, 32], [4, 33], [4, 34], [5, 6], [5, 14], [5, 21], [... | {"num_nodes": 60, "edges": [[0, 9], [0, 19], [0, 40], [0, 57], [1, 4], [1, 18], [1, 20], [1, 37], [1, 43], [1, 46], [1, 50], [1, 51], [2, 17], [2, 25], [2, 40], [2, 54], [3, 9], [3, 17], [3, 25], [3, 27], [3, 55], [4, 14], [4, 16], [4, 29], [4, 32], [4, 33], [4, 34], [5, 6], [5, 14], [5, 21], [5, 46], [5, 54], [6, 13],... | null | null | null | {"coloring": [1, 2, 1, 0, 1, 1, 2, 2, 1, 2, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 0]} | 1 |
construct-nppc-3col-l5-s5 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 2], [0, 34], [0, 39], [0, 45], [1, 13], [1, 32], [2, 3], [2, 13], [2, 15], [2, 24], [2, 41], [3, 10], [3, 18], [3, 37], [3, 42], [3, 44], [3, 47], [3, 53], [4, 8], [4, 17], [4, 22], [4, 23], [4, 31], [4, 35], [4, 42], [4, 48], [4, 53], [5, 27], [5, 32], [5, 37], ... | {"num_nodes": 60, "edges": [[0, 2], [0, 34], [0, 39], [0, 45], [1, 13], [1, 32], [2, 3], [2, 13], [2, 15], [2, 24], [2, 41], [3, 10], [3, 18], [3, 37], [3, 42], [3, 44], [3, 47], [3, 53], [4, 8], [4, 17], [4, 22], [4, 23], [4, 31], [4, 35], [4, 42], [4, 48], [4, 53], [5, 27], [5, 32], [5, 37], [5, 56], [6, 28], [6, 42]... | null | null | null | {"coloring": [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 2, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1]} | 1 |
construct-nppc-3col-l5-s6 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 1], [0, 22], [0, 37], [0, 43], [0, 45], [0, 59], [1, 3], [1, 17], [1, 27], [1, 33], [1, 54], [2, 6], [2, 23], [2, 30], [2, 34], [2, 54], [3, 12], [3, 16], [3, 20], [3, 31], [3, 35], [3, 40], [4, 5], [4, 14], [4, 20], [4, 31], [4, 34], [4, 42], [4, 55], [4, 56], [... | {"num_nodes": 60, "edges": [[0, 1], [0, 22], [0, 37], [0, 43], [0, 45], [0, 59], [1, 3], [1, 17], [1, 27], [1, 33], [1, 54], [2, 6], [2, 23], [2, 30], [2, 34], [2, 54], [3, 12], [3, 16], [3, 20], [3, 31], [3, 35], [3, 40], [4, 5], [4, 14], [4, 20], [4, 31], [4, 34], [4, 42], [4, 55], [4, 56], [5, 8], [5, 21], [5, 27], ... | null | null | null | {"coloring": [1, 2, 2, 0, 2, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 2, 1, 2, 2, 1, 2, 2, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2]} | 1 |
construct-nppc-3col-l5-s7 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 1], [0, 16], [0, 24], [0, 32], [0, 41], [0, 48], [1, 2], [1, 37], [1, 45], [1, 51], [1, 52], [1, 55], [2, 8], [2, 13], [2, 30], [2, 42], [2, 59], [3, 6], [3, 10], [3, 30], [3, 32], [3, 43], [3, 59], [4, 28], [4, 30], [4, 31], [4, 52], [5, 21], [5, 32], [5, 51], [... | {"num_nodes": 60, "edges": [[0, 1], [0, 16], [0, 24], [0, 32], [0, 41], [0, 48], [1, 2], [1, 37], [1, 45], [1, 51], [1, 52], [1, 55], [2, 8], [2, 13], [2, 30], [2, 42], [2, 59], [3, 6], [3, 10], [3, 30], [3, 32], [3, 43], [3, 59], [4, 28], [4, 30], [4, 31], [4, 52], [5, 21], [5, 32], [5, 51], [6, 12], [6, 38], [6, 39],... | null | null | null | {"coloring": [2, 0, 2, 2, 2, 1, 0, 1, 1, 2, 0, 1, 1, 0, 2, 0, 1, 2, 1, 2, 2, 2, 1, 0, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 2, 1, 1, 2, 1, 0, 2, 0, 1]} | 1 |
construct-nppc-3col-l5-s8 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 5], [0, 10], [0, 18], [0, 37], [0, 43], [0, 53], [1, 13], [1, 28], [1, 36], [1, 38], [1, 39], [1, 45], [2, 5], [2, 6], [2, 8], [2, 13], [2, 14], [2, 17], [2, 22], [2, 53], [2, 59], [3, 11], [3, 13], [3, 23], [3, 29], [3, 30], [3, 31], [3, 32], [3, 40], [3, 47], [... | {"num_nodes": 60, "edges": [[0, 5], [0, 10], [0, 18], [0, 37], [0, 43], [0, 53], [1, 13], [1, 28], [1, 36], [1, 38], [1, 39], [1, 45], [2, 5], [2, 6], [2, 8], [2, 13], [2, 14], [2, 17], [2, 22], [2, 53], [2, 59], [3, 11], [3, 13], [3, 23], [3, 29], [3, 30], [3, 31], [3, 32], [3, 40], [3, 47], [3, 48], [4, 7], [4, 15], ... | null | null | null | {"coloring": [1, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 2, 1, 2, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 2, 1, 2, 2, 1, 0, 1]} | 1 |
construct-nppc-3col-l5-s9 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 5 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 60 vertices labelled 0..59 and edge list
[[0, 11], [0, 13], [0, 38], [0, 44], [0, 45], [0, 46], [0, 49], [0, 50], [0, 55], [0, 59], [1, 2], [1, 12], [1, 15], [1, 17], [1, 18], [1, 26], [1, 41], [1, 44], [2, 23], [2, 26], [2, 49], [3, 18], [3, 28], [3, 39], [3, 45], [3, 56], [4, 24], [4, 26], [4, 28], [4, 44]... | {"num_nodes": 60, "edges": [[0, 11], [0, 13], [0, 38], [0, 44], [0, 45], [0, 46], [0, 49], [0, 50], [0, 55], [0, 59], [1, 2], [1, 12], [1, 15], [1, 17], [1, 18], [1, 26], [1, 41], [1, 44], [2, 23], [2, 26], [2, 49], [3, 18], [3, 28], [3, 39], [3, 45], [3, 56], [4, 24], [4, 26], [4, 28], [4, 44], [5, 16], [5, 17], [5, 1... | null | null | null | {"coloring": [2, 0, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 1]} | 1 |
construct-nppc-3col-l6-s0 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 23], [0, 29], [0, 33], [0, 36], [0, 65], [0, 67], [0, 81], [0, 84], [0, 85], [0, 116], [1, 2], [1, 8], [1, 16], [1, 24], [1, 30], [1, 61], [1, 66], [1, 77], [1, 86], [1, 95], [2, 30], [2, 51], [2, 52], [2, 64], [2, 89], [3, 5], [3, 27], [3, 41], [3, 45], [3, 61... | {"num_nodes": 120, "edges": [[0, 23], [0, 29], [0, 33], [0, 36], [0, 65], [0, 67], [0, 81], [0, 84], [0, 85], [0, 116], [1, 2], [1, 8], [1, 16], [1, 24], [1, 30], [1, 61], [1, 66], [1, 77], [1, 86], [1, 95], [2, 30], [2, 51], [2, 52], [2, 64], [2, 89], [3, 5], [3, 27], [3, 41], [3, 45], [3, 61], [3, 63], [3, 75], [3, 7... | null | null | null | {"coloring": [1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 2, 1, 2, 0, 2, 2, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 2, 1, 1, 2, 1, 0, 2, 1, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, ... | 1 |
construct-nppc-3col-l6-s1 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 10], [0, 23], [0, 29], [0, 45], [0, 46], [0, 54], [0, 73], [0, 78], [0, 100], [0, 101], [1, 3], [1, 7], [1, 33], [1, 44], [1, 72], [1, 112], [2, 7], [2, 10], [2, 14], [2, 27], [2, 28], [2, 53], [2, 54], [2, 70], [2, 79], [2, 104], [2, 108], [3, 4], [3, 6], [3, ... | {"num_nodes": 120, "edges": [[0, 10], [0, 23], [0, 29], [0, 45], [0, 46], [0, 54], [0, 73], [0, 78], [0, 100], [0, 101], [1, 3], [1, 7], [1, 33], [1, 44], [1, 72], [1, 112], [2, 7], [2, 10], [2, 14], [2, 27], [2, 28], [2, 53], [2, 54], [2, 70], [2, 79], [2, 104], [2, 108], [3, 4], [3, 6], [3, 25], [3, 30], [3, 31], [3,... | null | null | null | {"coloring": [2, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 1, 1, 0, 2, 0, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, ... | 1 |
construct-nppc-3col-l6-s2 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 9], [0, 46], [0, 61], [0, 63], [0, 97], [1, 33], [1, 36], [1, 57], [1, 79], [1, 102], [1, 105], [2, 16], [2, 26], [2, 28], [2, 35], [2, 40], [2, 43], [2, 48], [2, 56], [2, 65], [2, 83], [2, 89], [3, 10], [3, 17], [3, 32], [3, 35], [3, 40], [3, 56], [3, 59], [3,... | {"num_nodes": 120, "edges": [[0, 9], [0, 46], [0, 61], [0, 63], [0, 97], [1, 33], [1, 36], [1, 57], [1, 79], [1, 102], [1, 105], [2, 16], [2, 26], [2, 28], [2, 35], [2, 40], [2, 43], [2, 48], [2, 56], [2, 65], [2, 83], [2, 89], [3, 10], [3, 17], [3, 32], [3, 35], [3, 40], [3, 56], [3, 59], [3, 70], [3, 85], [3, 99], [3... | null | null | null | {"coloring": [2, 0, 1, 2, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 1, 0, 1, 1, 0, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2, 1, 1, 1, 1, 1, 2, ... | 1 |
construct-nppc-3col-l6-s3 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 11], [0, 16], [0, 20], [0, 68], [0, 85], [0, 118], [1, 19], [1, 30], [1, 33], [1, 40], [1, 45], [1, 53], [1, 64], [1, 70], [1, 81], [1, 93], [1, 103], [1, 105], [1, 117], [2, 16], [2, 27], [2, 33], [2, 45], [2, 47], [2, 64], [2, 71], [2, 87], [2, 99], [2, 119],... | {"num_nodes": 120, "edges": [[0, 11], [0, 16], [0, 20], [0, 68], [0, 85], [0, 118], [1, 19], [1, 30], [1, 33], [1, 40], [1, 45], [1, 53], [1, 64], [1, 70], [1, 81], [1, 93], [1, 103], [1, 105], [1, 117], [2, 16], [2, 27], [2, 33], [2, 45], [2, 47], [2, 64], [2, 71], [2, 87], [2, 99], [2, 119], [3, 8], [3, 9], [3, 14], ... | null | null | null | {"coloring": [1, 0, 1, 2, 1, 0, 2, 0, 1, 1, 1, 2, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 2, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 2, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, ... | 1 |
construct-nppc-3col-l6-s4 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 19], [0, 34], [0, 51], [0, 53], [0, 60], [0, 73], [0, 97], [0, 109], [1, 2], [1, 7], [1, 30], [1, 39], [1, 53], [1, 54], [1, 76], [1, 88], [1, 111], [1, 118], [2, 6], [2, 16], [2, 35], [2, 73], [2, 86], [2, 92], [2, 95], [3, 28], [3, 86], [3, 98], [3, 112], [4,... | {"num_nodes": 120, "edges": [[0, 19], [0, 34], [0, 51], [0, 53], [0, 60], [0, 73], [0, 97], [0, 109], [1, 2], [1, 7], [1, 30], [1, 39], [1, 53], [1, 54], [1, 76], [1, 88], [1, 111], [1, 118], [2, 6], [2, 16], [2, 35], [2, 73], [2, 86], [2, 92], [2, 95], [3, 28], [3, 86], [3, 98], [3, 112], [4, 78], [4, 83], [4, 91], [4... | null | null | null | {"coloring": [1, 1, 0, 2, 2, 0, 1, 2, 1, 2, 0, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 1, 2, 0, 1, 1, 1, 2, 2, 2, 0, 1, 1, 2, 2, 1, 2, 0, 0, 1, 2, 2, ... | 1 |
construct-nppc-3col-l6-s5 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 19], [0, 46], [0, 66], [0, 82], [0, 84], [0, 90], [0, 97], [1, 21], [1, 34], [1, 36], [1, 66], [1, 83], [1, 84], [1, 91], [1, 100], [2, 26], [2, 32], [2, 74], [2, 85], [2, 91], [2, 107], [3, 71], [3, 74], [3, 98], [3, 108], [4, 27], [4, 42], [4, 74], [4, 76], [... | {"num_nodes": 120, "edges": [[0, 19], [0, 46], [0, 66], [0, 82], [0, 84], [0, 90], [0, 97], [1, 21], [1, 34], [1, 36], [1, 66], [1, 83], [1, 84], [1, 91], [1, 100], [2, 26], [2, 32], [2, 74], [2, 85], [2, 91], [2, 107], [3, 71], [3, 74], [3, 98], [3, 108], [4, 27], [4, 42], [4, 74], [4, 76], [4, 93], [4, 96], [4, 106],... | null | null | null | {"coloring": [2, 1, 1, 2, 1, 2, 1, 2, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 2, 1, 0, 0, 1, 2, 0, 2, 2, 2, 1, 0, 1, 1, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 1, 2, 0, 1, 1, 2, 1, 0, 0, 1, 1, 1, 2, 2, 2, 1, 0, 2, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 1, 0, 1, ... | 1 |
construct-nppc-3col-l6-s6 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 2], [0, 7], [0, 11], [0, 21], [0, 69], [0, 96], [0, 112], [1, 19], [1, 45], [1, 49], [1, 94], [1, 104], [1, 109], [1, 113], [1, 114], [1, 116], [2, 33], [2, 39], [2, 82], [2, 86], [2, 87], [2, 107], [2, 118], [3, 8], [3, 13], [3, 17], [3, 28], [3, 40], [3, 50],... | {"num_nodes": 120, "edges": [[0, 2], [0, 7], [0, 11], [0, 21], [0, 69], [0, 96], [0, 112], [1, 19], [1, 45], [1, 49], [1, 94], [1, 104], [1, 109], [1, 113], [1, 114], [1, 116], [2, 33], [2, 39], [2, 82], [2, 86], [2, 87], [2, 107], [2, 118], [3, 8], [3, 13], [3, 17], [3, 28], [3, 40], [3, 50], [3, 75], [3, 76], [3, 102... | null | null | null | {"coloring": [0, 0, 1, 2, 1, 0, 2, 1, 0, 1, 1, 1, 2, 1, 2, 0, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1, 1, 1, 2, 1, 2, 0, 2, 0, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, ... | 1 |
construct-nppc-3col-l6-s7 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 13], [0, 16], [0, 45], [0, 64], [0, 66], [0, 72], [0, 91], [0, 99], [0, 104], [0, 109], [0, 116], [1, 15], [1, 20], [1, 33], [1, 45], [1, 50], [1, 56], [1, 60], [1, 80], [2, 3], [2, 10], [2, 20], [2, 31], [2, 54], [2, 62], [2, 76], [2, 78], [2, 103], [2, 114], ... | {"num_nodes": 120, "edges": [[0, 13], [0, 16], [0, 45], [0, 64], [0, 66], [0, 72], [0, 91], [0, 99], [0, 104], [0, 109], [0, 116], [1, 15], [1, 20], [1, 33], [1, 45], [1, 50], [1, 56], [1, 60], [1, 80], [2, 3], [2, 10], [2, 20], [2, 31], [2, 54], [2, 62], [2, 76], [2, 78], [2, 103], [2, 114], [3, 14], [3, 42], [3, 48],... | null | null | null | {"coloring": [0, 2, 2, 1, 2, 0, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 1, 1, 0, 2, 2, 1, 2, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 2, 0, 2, 0, 1, ... | 1 |
construct-nppc-3col-l6-s8 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 24], [0, 42], [0, 60], [0, 93], [1, 7], [1, 25], [1, 28], [1, 29], [1, 61], [1, 74], [1, 82], [1, 107], [2, 16], [2, 18], [2, 21], [2, 24], [2, 28], [2, 33], [2, 39], [2, 71], [2, 96], [2, 112], [2, 114], [3, 12], [3, 20], [3, 44], [3, 64], [3, 66], [3, 82], [3... | {"num_nodes": 120, "edges": [[0, 24], [0, 42], [0, 60], [0, 93], [1, 7], [1, 25], [1, 28], [1, 29], [1, 61], [1, 74], [1, 82], [1, 107], [2, 16], [2, 18], [2, 21], [2, 24], [2, 28], [2, 33], [2, 39], [2, 71], [2, 96], [2, 112], [2, 114], [3, 12], [3, 20], [3, 44], [3, 64], [3, 66], [3, 82], [3, 86], [3, 92], [3, 104], ... | null | null | null | {"coloring": [2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 2, 2, 1, 0, 2, 2, 1, 2, 0, 0, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 1, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 2, 1, ... | 1 |
construct-nppc-3col-l6-s9 | construct | nppc_three_coloring | graph_3_coloring | graph_theory | competition | 6 | NPPC/graph_three_colorability | MIT | [
"agentic_trivial",
"np_search"
] | Graph with 120 vertices labelled 0..119 and edge list
[[0, 4], [0, 19], [0, 21], [0, 105], [1, 5], [1, 13], [1, 17], [1, 24], [1, 46], [1, 47], [1, 62], [1, 63], [1, 75], [1, 81], [1, 90], [1, 102], [2, 11], [2, 18], [2, 30], [2, 59], [2, 62], [2, 72], [2, 75], [2, 95], [3, 11], [3, 17], [3, 20], [3, 30], [3, 36], [3, ... | {"num_nodes": 120, "edges": [[0, 4], [0, 19], [0, 21], [0, 105], [1, 5], [1, 13], [1, 17], [1, 24], [1, 46], [1, 47], [1, 62], [1, 63], [1, 75], [1, 81], [1, 90], [1, 102], [2, 11], [2, 18], [2, 30], [2, 59], [2, 62], [2, 72], [2, 75], [2, 95], [3, 11], [3, 17], [3, 20], [3, 30], [3, 36], [3, 66], [3, 74], [3, 100], [4... | null | null | null | {"coloring": [1, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 2, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 2, 2, 0, 1, 0, 0, 1, 1, 2, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 2, 2, 2, 1, 1, 1, 0, 2, 1, 2, 0, 2, 1, 1, 0, 0, 2, 0, 2, 2, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 0, 1, 2, ... | 1 |
construct-nppc-vertex-cover-l1-s0 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 14 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [2, 3], [2, 5], [2, 6], [2, 7], [3, 7], [5, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover"... | {"num_nodes": 8, "k": 3, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 7], [2, 3], [2, 5], [2, 6], [2, 7], [3, 7], [5, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [0, 2, 7]} | 1 |
construct-nppc-vertex-cover-l1-s1 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 10 edges:
[[0, 3], [0, 4], [0, 5], [1, 4], [1, 7], [2, 4], [3, 4], [4, 5], [4, 6], [4, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, v_2, ...]} (distinct int... | {"num_nodes": 8, "k": 3, "edges": [[0, 3], [0, 4], [0, 5], [1, 4], [1, 7], [2, 4], [3, 4], [4, 5], [4, 6], [4, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [0, 1, 4]} | 1 |
construct-nppc-vertex-cover-l1-s2 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 11 edges:
[[0, 2], [0, 3], [1, 4], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, v_2, ...]} (dist... | {"num_nodes": 8, "k": 3, "edges": [[0, 2], [0, 3], [1, 4], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [2, 3, 4]} | 1 |
construct-nppc-vertex-cover-l1-s3 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 13 edges:
[[0, 1], [0, 5], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [3, 4], [4, 6], [5, 6], [5, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, ... | {"num_nodes": 8, "k": 3, "edges": [[0, 1], [0, 5], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [3, 4], [4, 6], [5, 6], [5, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [1, 4, 5]} | 1 |
construct-nppc-vertex-cover-l1-s4 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 14 edges:
[[0, 4], [0, 7], [1, 2], [1, 7], [2, 3], [2, 4], [2, 6], [2, 7], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7], [5, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover"... | {"num_nodes": 8, "k": 3, "edges": [[0, 4], [0, 7], [1, 2], [1, 7], [2, 3], [2, 4], [2, 6], [2, 7], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7], [5, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [2, 4, 7]} | 1 |
construct-nppc-vertex-cover-l1-s5 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 10 edges:
[[0, 2], [0, 4], [1, 2], [2, 3], [2, 5], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, v_2, ...]} (distinct int... | {"num_nodes": 8, "k": 3, "edges": [[0, 2], [0, 4], [1, 2], [2, 3], [2, 5], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [2, 3, 4]} | 1 |
construct-nppc-vertex-cover-l1-s6 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 11 edges:
[[0, 2], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [2, 6], [3, 4], [4, 5], [4, 6], [4, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, v_2, ...]} (dist... | {"num_nodes": 8, "k": 3, "edges": [[0, 2], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [2, 6], [3, 4], [4, 5], [4, 6], [4, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [2, 3, 4]} | 1 |
construct-nppc-vertex-cover-l1-s7 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 12 edges:
[[0, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [2, 5], [2, 6], [3, 5], [4, 5], [5, 6], [5, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, v_2, ...... | {"num_nodes": 8, "k": 3, "edges": [[0, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [2, 5], [2, 6], [3, 5], [4, 5], [5, 6], [5, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [1, 5, 6]} | 1 |
construct-nppc-vertex-cover-l1-s8 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 14 edges:
[[0, 4], [0, 5], [1, 5], [1, 7], [2, 5], [2, 7], [3, 4], [3, 5], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover"... | {"num_nodes": 8, "k": 3, "edges": [[0, 4], [0, 5], [1, 5], [1, 7], [2, 5], [2, 7], [3, 4], [3, 5], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [4, 5, 7]} | 1 |
construct-nppc-vertex-cover-l1-s9 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 1 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 8 vertices labelled 0..7 and 12 edges:
[[0, 4], [0, 7], [1, 7], [2, 5], [2, 7], [3, 4], [3, 5], [3, 7], [4, 5], [4, 7], [5, 7], [6, 7]]
Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
Answer format: {"cover": [v_1, v_2, ...... | {"num_nodes": 8, "k": 3, "edges": [[0, 4], [0, 7], [1, 7], [2, 5], [2, 7], [3, 4], [3, 5], [3, 7], [4, 5], [4, 7], [5, 7], [6, 7]], "family": "nppc_vertex_cover", "subset": "construct"} | null | null | null | {"cover": [4, 5, 7]} | 1 |
construct-nppc-vertex-cover-l2-s0 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 40 edges:
[[0, 9], [0, 10], [0, 11], [1, 3], [1, 7], [1, 10], [2, 3], [2, 7], [2, 10], [2, 11], [3, 7], [3, 9], [3, 10], [3, 11], [3, 13], [3, 14], [4, 7], [4, 10], [4, 11], [5, 7], [5, 11], [6, 7], [7, 10], [7, 11], [7, 12], [7, 15], [8, 9], [8, 10], [9, 10], [9, 11... | {"num_nodes": 16, "k": 5, "edges": [[0, 9], [0, 10], [0, 11], [1, 3], [1, 7], [1, 10], [2, 3], [2, 7], [2, 10], [2, 11], [3, 7], [3, 9], [3, 10], [3, 11], [3, 13], [3, 14], [4, 7], [4, 10], [4, 11], [5, 7], [5, 11], [6, 7], [7, 10], [7, 11], [7, 12], [7, 15], [8, 9], [8, 10], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14]... | null | null | null | {"cover": [3, 7, 9, 10, 11]} | 1 |
construct-nppc-vertex-cover-l2-s1 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 46 edges:
[[0, 1], [0, 4], [0, 6], [0, 7], [0, 8], [0, 10], [0, 11], [0, 13], [0, 14], [1, 8], [1, 10], [1, 12], [2, 8], [2, 13], [3, 8], [3, 10], [3, 13], [4, 8], [4, 12], [4, 13], [5, 10], [5, 12], [6, 8], [6, 12], [6, 13], [7, 10], [7, 12], [8, 9], [8, 10], [8, 11... | {"num_nodes": 16, "k": 5, "edges": [[0, 1], [0, 4], [0, 6], [0, 7], [0, 8], [0, 10], [0, 11], [0, 13], [0, 14], [1, 8], [1, 10], [1, 12], [2, 8], [2, 13], [3, 8], [3, 10], [3, 13], [4, 8], [4, 12], [4, 13], [5, 10], [5, 12], [6, 8], [6, 12], [6, 13], [7, 10], [7, 12], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 15]... | null | null | null | {"cover": [0, 8, 10, 12, 13]} | 1 |
construct-nppc-vertex-cover-l2-s2 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 43 edges:
[[0, 7], [0, 12], [1, 2], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 9], [2, 10], [2, 11], [2, 14], [2, 15], [3, 7], [3, 13], [5, 7], [5, 14], [6, 13], [6, 14], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [8, 12], [8, 13... | {"num_nodes": 16, "k": 5, "edges": [[0, 7], [0, 12], [1, 2], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 9], [2, 10], [2, 11], [2, 14], [2, 15], [3, 7], [3, 13], [5, 7], [5, 14], [6, 13], [6, 14], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [8, 12], [8, 13], [8, 14], [9, 12], [9, 13]... | null | null | null | {"cover": [2, 7, 12, 13, 14]} | 1 |
construct-nppc-vertex-cover-l2-s3 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 43 edges:
[[0, 1], [0, 5], [0, 7], [0, 8], [0, 12], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 12], [1, 13], [1, 15], [2, 7], [2, 8], [3, 7], [3, 8], [3, 12], [4, 7], [4, 8], [4, 12], [5, 9], [5, 10], [5, 11], [5, 12], [5, 14], [5, 15], [6, 7], [7, 8... | {"num_nodes": 16, "k": 5, "edges": [[0, 1], [0, 5], [0, 7], [0, 8], [0, 12], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 12], [1, 13], [1, 15], [2, 7], [2, 8], [3, 7], [3, 8], [3, 12], [4, 7], [4, 8], [4, 12], [5, 9], [5, 10], [5, 11], [5, 12], [5, 14], [5, 15], [6, 7], [7, 8], [7, 9], [7, 10], [7, 12],... | null | null | null | {"cover": [1, 5, 7, 8, 12]} | 1 |
construct-nppc-vertex-cover-l2-s4 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 37 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 11], [0, 12], [0, 13], [0, 14], [1, 6], [1, 13], [2, 3], [2, 6], [3, 5], [3, 6], [3, 8], [3, 9], [3, 10], [3, 12], [3, 13], [3, 15], [4, 11], [4, 12], [4, 13], [4, 14], [5, 13], [6, 8], [6, 9], [6... | {"num_nodes": 16, "k": 5, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 11], [0, 12], [0, 13], [0, 14], [1, 6], [1, 13], [2, 3], [2, 6], [3, 5], [3, 6], [3, 8], [3, 9], [3, 10], [3, 12], [3, 13], [3, 15], [4, 11], [4, 12], [4, 13], [4, 14], [5, 13], [6, 8], [6, 9], [6, 11], [6, 13], [6, 14], [7,... | null | null | null | {"cover": [0, 3, 4, 6, 13]} | 1 |
construct-nppc-vertex-cover-l2-s5 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 44 edges:
[[0, 2], [0, 7], [0, 12], [1, 2], [1, 7], [1, 12], [2, 4], [2, 5], [2, 7], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 5], [3, 7], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [4, 10], [4, 12], [5, 10], [5, 12], [6, 7], [6, 10]... | {"num_nodes": 16, "k": 5, "edges": [[0, 2], [0, 7], [0, 12], [1, 2], [1, 7], [1, 12], [2, 4], [2, 5], [2, 7], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 5], [3, 7], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [4, 10], [4, 12], [5, 10], [5, 12], [6, 7], [6, 10], [6, 12], [7, 8], [7, 9], [... | null | null | null | {"cover": [2, 3, 7, 10, 12]} | 1 |
construct-nppc-vertex-cover-l2-s6 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 29 edges:
[[0, 6], [1, 2], [1, 4], [1, 8], [1, 15], [3, 6], [3, 10], [4, 5], [4, 8], [4, 10], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 15], [6, 8], [6, 9], [6, 10], [6, 11], [6, 14], [7, 8], [8, 11], [8, 12], [9, 10], [10, 11], [10, 12], [10, 13], [10, 15]]
Fi... | {"num_nodes": 16, "k": 5, "edges": [[0, 6], [1, 2], [1, 4], [1, 8], [1, 15], [3, 6], [3, 10], [4, 5], [4, 8], [4, 10], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 15], [6, 8], [6, 9], [6, 10], [6, 11], [6, 14], [7, 8], [8, 11], [8, 12], [9, 10], [10, 11], [10, 12], [10, 13], [10, 15]], "family": "nppc_vertex_cover",... | null | null | null | {"cover": [1, 5, 6, 8, 10]} | 1 |
construct-nppc-vertex-cover-l2-s7 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 43 edges:
[[0, 1], [0, 2], [0, 3], [0, 5], [0, 8], [0, 10], [0, 11], [0, 12], [0, 13], [1, 11], [1, 13], [2, 3], [2, 13], [3, 4], [3, 5], [3, 9], [3, 10], [3, 11], [3, 13], [4, 9], [4, 11], [4, 13], [5, 9], [5, 11], [5, 13], [6, 11], [6, 13], [7, 9], [7, 11], [7, 13]... | {"num_nodes": 16, "k": 5, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 8], [0, 10], [0, 11], [0, 12], [0, 13], [1, 11], [1, 13], [2, 3], [2, 13], [3, 4], [3, 5], [3, 9], [3, 10], [3, 11], [3, 13], [4, 9], [4, 11], [4, 13], [5, 9], [5, 11], [5, 13], [6, 11], [6, 13], [7, 9], [7, 11], [7, 13], [8, 9], [8, 11], [8, 13], ... | null | null | null | {"cover": [0, 3, 9, 11, 13]} | 1 |
construct-nppc-vertex-cover-l2-s8 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 45 edges:
[[0, 2], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 14], [1, 8], [1, 9], [1, 13], [1, 15], [2, 8], [2, 9], [2, 13], [2, 15], [3, 9], [3, 13], [3, 15], [4, 8], [4, 9], [4, 13], [5, 15], [6, 8], [6, 9], [6, 13], [6, 15], [7, 8], [7, 13], [7... | {"num_nodes": 16, "k": 5, "edges": [[0, 2], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 14], [1, 8], [1, 9], [1, 13], [1, 15], [2, 8], [2, 9], [2, 13], [2, 15], [3, 9], [3, 13], [3, 15], [4, 8], [4, 9], [4, 13], [5, 15], [6, 8], [6, 9], [6, 13], [6, 15], [7, 8], [7, 13], [7, 15], [8, 9], [8, 11], [8, ... | null | null | null | {"cover": [0, 8, 9, 13, 15]} | 1 |
construct-nppc-vertex-cover-l2-s9 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 2 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 16 vertices labelled 0..15 and 40 edges:
[[0, 2], [0, 4], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [2, 6], [2, 9], [2, 10], [2, 13], [2, 14], [3, 4], [3, 12], [4, 5], [4, 6], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 15], [... | {"num_nodes": 16, "k": 5, "edges": [[0, 2], [0, 4], [0, 15], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [2, 6], [2, 9], [2, 10], [2, 13], [2, 14], [3, 4], [3, 12], [4, 5], [4, 6], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 15], [5, 15], [6, 15], [7, 12], [7... | null | null | null | {"cover": [1, 2, 4, 12, 15]} | 1 |
construct-nppc-vertex-cover-l3-s0 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 134 edges:
[[0, 1], [0, 2], [0, 4], [0, 5], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 20], [0, 21], [0, 23], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 15], [1, 16], [1, 17], [1, 18], [1, 20],... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 20], [0, 21], [0, 23], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 15], [1, 16], [1, 17], [1, 18], [1, 20], [1, 21], [1, 22], [1, 23], ... | null | null | null | {"cover": [0, 1, 4, 7, 8, 10, 14, 17, 18, 21, 22, 23]} | 1 |
construct-nppc-vertex-cover-l3-s1 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 131 edges:
[[0, 1], [0, 2], [0, 3], [0, 12], [0, 14], [0, 17], [0, 20], [1, 2], [1, 6], [1, 7], [1, 8], [1, 12], [1, 13], [1, 14], [1, 15], [1, 17], [1, 20], [1, 23], [2, 3], [2, 4], [2, 6], [2, 8], [2, 9], [2, 10], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 12], [0, 14], [0, 17], [0, 20], [1, 2], [1, 6], [1, 7], [1, 8], [1, 12], [1, 13], [1, 14], [1, 15], [1, 17], [1, 20], [1, 23], [2, 3], [2, 4], [2, 6], [2, 8], [2, 9], [2, 10], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22]... | null | null | null | {"cover": [1, 2, 3, 5, 8, 12, 14, 16, 17, 20, 22, 23]} | 1 |
construct-nppc-vertex-cover-l3-s2 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 121 edges:
[[0, 1], [0, 3], [0, 6], [0, 7], [0, 9], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 20], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 10], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [2, 6], [2, 13], [2, 15], [2, 1... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 3], [0, 6], [0, 7], [0, 9], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 20], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 10], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [2, 6], [2, 13], [2, 15], [2, 16], [2, 19], [2, 20], [3, 5]... | null | null | null | {"cover": [0, 1, 5, 6, 13, 15, 16, 17, 18, 19, 20, 23]} | 1 |
construct-nppc-vertex-cover-l3-s3 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 113 edges:
[[0, 1], [0, 2], [0, 3], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [1, 2], [1, 7], [1, 14], [1, 18], [1, 19], [1, 22], [2, 3], [2, 4], [2, 5], [2, 8], [2, 11], [2, 12], [2, 13], [2, 16... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 15], [0, 17], [0, 18], [0, 19], [0, 21], [0, 22], [0, 23], [1, 2], [1, 7], [1, 14], [1, 18], [1, 19], [1, 22], [2, 3], [2, 4], [2, 5], [2, 8], [2, 11], [2, 12], [2, 13], [2, 16], [2, 17], [2, 18], [2, 23]... | null | null | null | {"cover": [0, 2, 7, 8, 9, 12, 14, 17, 18, 19, 20, 22]} | 1 |
construct-nppc-vertex-cover-l3-s4 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 124 edges:
[[0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 9], [0, 10], [0, 12], [0, 13], [0, 14], [0, 15], [0, 18], [0, 20], [0, 21], [0, 23], [1, 4], [1, 6], [1, 7], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 20], [1, 21], [2, 9], [2, 11], [2, 20], [3, ... | {"num_nodes": 24, "k": 12, "edges": [[0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 9], [0, 10], [0, 12], [0, 13], [0, 14], [0, 15], [0, 18], [0, 20], [0, 21], [0, 23], [1, 4], [1, 6], [1, 7], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 20], [1, 21], [2, 9], [2, 11], [2, 20], [3, 5], [3, 7], [3, 9], [3, 11],... | null | null | null | {"cover": [0, 1, 4, 5, 6, 7, 9, 10, 11, 15, 17, 20]} | 1 |
construct-nppc-vertex-cover-l3-s5 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 128 edges:
[[0, 4], [0, 7], [0, 8], [0, 14], [0, 15], [1, 4], [1, 8], [1, 9], [1, 13], [1, 17], [1, 18], [2, 4], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 21], [2, 22], [2, 23], [3, 4], [3, 8... | {"num_nodes": 24, "k": 12, "edges": [[0, 4], [0, 7], [0, 8], [0, 14], [0, 15], [1, 4], [1, 8], [1, 9], [1, 13], [1, 17], [1, 18], [2, 4], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 21], [2, 22], [2, 23], [3, 4], [3, 8], [3, 9], [3, 15], [3, 16],... | null | null | null | {"cover": [2, 4, 7, 8, 9, 13, 14, 15, 16, 17, 18, 21]} | 1 |
construct-nppc-vertex-cover-l3-s6 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 122 edges:
[[0, 1], [0, 5], [0, 7], [0, 10], [0, 20], [0, 21], [0, 23], [1, 2], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 15], [1, 16], [1, 17], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 10], [3, 11], [3, 15], [3... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 5], [0, 7], [0, 10], [0, 20], [0, 21], [0, 23], [1, 2], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 15], [1, 16], [1, 17], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 10], [3, 11], [3, 15], [3, 16], [3, 18], [3, 19], [3,... | null | null | null | {"cover": [1, 3, 4, 5, 6, 7, 10, 15, 19, 20, 21, 23]} | 1 |
construct-nppc-vertex-cover-l3-s7 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 139 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 16], [0, 18], [0, 20], [0, 23], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 20], [1, 21], [1, 22], [2, 4], ... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 16], [0, 18], [0, 20], [0, 23], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 20], [1, 21], [1, 22], [2, 4], [2, 7], [2, 8], [2, 9], [2, ... | null | null | null | {"cover": [0, 1, 2, 5, 6, 8, 12, 13, 16, 20, 22, 23]} | 1 |
construct-nppc-vertex-cover-l3-s8 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 133 edges:
[[0, 1], [0, 3], [0, 9], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 23], [1, 2], [1, 3], [1, 4], [1, 5], [1, 8], [1, 10], [1, 11], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [2, 3], [2, 8], [2, 10], [2, ... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 3], [0, 9], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 23], [1, 2], [1, 3], [1, 4], [1, 5], [1, 8], [1, 10], [1, 11], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [2, 3], [2, 8], [2, 10], [2, 13], [2, 15], [2, 19], [2, 2... | null | null | null | {"cover": [1, 3, 8, 9, 10, 13, 15, 16, 17, 18, 19, 23]} | 1 |
construct-nppc-vertex-cover-l3-s9 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 3 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 24 vertices labelled 0..23 and 121 edges:
[[0, 1], [0, 2], [0, 4], [0, 8], [0, 10], [0, 11], [0, 12], [0, 16], [1, 2], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 18], [1, 19], [1, 20], [1, 22], [2, 3], [2, 5], [2, 7], [2, 8], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14]... | {"num_nodes": 24, "k": 12, "edges": [[0, 1], [0, 2], [0, 4], [0, 8], [0, 10], [0, 11], [0, 12], [0, 16], [1, 2], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 12], [1, 13], [1, 14], [1, 18], [1, 19], [1, 20], [1, 22], [2, 3], [2, 5], [2, 7], [2, 8], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 19], [2, 20], [2, 21],... | null | null | null | {"cover": [1, 2, 4, 7, 8, 10, 11, 12, 14, 16, 18, 23]} | 1 |
construct-nppc-vertex-cover-l4-s0 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 352 edges:
[[0, 6], [0, 9], [0, 11], [0, 17], [0, 19], [0, 21], [0, 24], [0, 25], [0, 26], [0, 30], [0, 31], [0, 35], [0, 37], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [1, 13], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 25], [1, 26], [1, 27], [... | {"num_nodes": 40, "k": 20, "edges": [[0, 6], [0, 9], [0, 11], [0, 17], [0, 19], [0, 21], [0, 24], [0, 25], [0, 26], [0, 30], [0, 31], [0, 35], [0, 37], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [1, 13], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 31], [1... | null | null | null | {"cover": [1, 6, 7, 9, 11, 12, 13, 17, 19, 21, 23, 24, 25, 26, 30, 31, 35, 37, 38, 39]} | 1 |
construct-nppc-vertex-cover-l4-s1 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 355 edges:
[[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 12], [0, 14], [0, 15], [0, 18], [0, 19], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [1, 8], [1, 13], [1, 18], [... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 12], [0, 14], [0, 15], [0, 18], [0, 19], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [1, 8], [1, 13], [1, 18], [1, 23], [1, 24], [1, 25], [1... | null | null | null | {"cover": [0, 5, 8, 12, 13, 14, 16, 17, 18, 22, 23, 24, 25, 27, 30, 31, 35, 36, 37, 39]} | 1 |
construct-nppc-vertex-cover-l4-s2 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 358 edges:
[[0, 1], [0, 7], [0, 8], [0, 9], [0, 13], [0, 15], [0, 22], [0, 26], [0, 34], [0, 35], [0, 36], [0, 38], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 26], [1, 2... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 7], [0, 8], [0, 9], [0, 13], [0, 15], [0, 22], [0, 26], [0, 34], [0, 35], [0, 36], [0, 38], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30... | null | null | null | {"cover": [1, 3, 7, 8, 9, 13, 15, 17, 18, 22, 26, 28, 29, 30, 31, 34, 35, 36, 38, 39]} | 1 |
construct-nppc-vertex-cover-l4-s3 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 344 edges:
[[0, 4], [0, 8], [0, 17], [0, 21], [0, 24], [0, 27], [0, 28], [0, 29], [0, 37], [0, 39], [1, 3], [1, 6], [1, 8], [1, 11], [1, 12], [1, 14], [1, 17], [1, 20], [1, 21], [1, 23], [1, 26], [1, 27], [1, 39], [2, 6], [2, 11], [2, 12], [2, 17], [2, 24], [2, 27], ... | {"num_nodes": 40, "k": 20, "edges": [[0, 4], [0, 8], [0, 17], [0, 21], [0, 24], [0, 27], [0, 28], [0, 29], [0, 37], [0, 39], [1, 3], [1, 6], [1, 8], [1, 11], [1, 12], [1, 14], [1, 17], [1, 20], [1, 21], [1, 23], [1, 26], [1, 27], [1, 39], [2, 6], [2, 11], [2, 12], [2, 17], [2, 24], [2, 27], [2, 28], [2, 29], [2, 37], [... | null | null | null | {"cover": [3, 4, 6, 8, 11, 12, 14, 16, 17, 20, 21, 23, 24, 26, 27, 28, 29, 33, 37, 39]} | 1 |
construct-nppc-vertex-cover-l4-s4 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 345 edges:
[[0, 1], [0, 2], [0, 3], [0, 8], [0, 9], [0, 11], [0, 12], [0, 19], [0, 20], [0, 23], [0, 33], [0, 37], [1, 3], [1, 4], [1, 7], [1, 8], [1, 9], [1, 11], [1, 14], [1, 16], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 28], [1, ... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 8], [0, 9], [0, 11], [0, 12], [0, 19], [0, 20], [0, 23], [0, 33], [0, 37], [1, 3], [1, 4], [1, 7], [1, 8], [1, 9], [1, 11], [1, 14], [1, 16], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 28], [1, 31], [1, 33], [1, 34], [1, 3... | null | null | null | {"cover": [1, 2, 3, 4, 8, 9, 11, 12, 18, 19, 20, 21, 23, 25, 31, 33, 35, 36, 37, 39]} | 1 |
construct-nppc-vertex-cover-l4-s5 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 340 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 16], [0, 17], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 30], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 39], [1, 2], [1, 4], [1... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 16], [0, 17], [0, 21], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 30], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 39], [1, 2], [1, 4], [1, 6], [1, 9], [1, 10], [1, 1... | null | null | null | {"cover": [0, 1, 2, 4, 6, 10, 11, 14, 16, 17, 21, 22, 23, 26, 29, 30, 31, 32, 33, 38]} | 1 |
construct-nppc-vertex-cover-l4-s6 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 347 edges:
[[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 23], [0, 24], [0, 25], [0, 27], [0, 28], [0, 29], [0, 31], [0, 32], [0, 33], [0, 35], [0, 36], [0, 37], [0, 38], [0... | {"num_nodes": 40, "k": 20, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 23], [0, 24], [0, 25], [0, 27], [0, 28], [0, 29], [0, 31], [0, 32], [0, 33], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [1, 17], [1, 19], [1,... | null | null | null | {"cover": [0, 5, 6, 7, 8, 9, 12, 17, 18, 19, 20, 21, 22, 25, 27, 29, 32, 34, 35, 37]} | 1 |
construct-nppc-vertex-cover-l4-s7 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 367 edges:
[[0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 37], [0, 39], [1, 4], [1, 7], [1, 9], [1,... | {"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 32], [0, 33], [0, 37], [0, 39], [1, 4], [1, 7], [1, 9], [1, 10], [1, 11], [1, 12], [1, ... | null | null | null | {"cover": [0, 1, 2, 4, 6, 7, 8, 10, 11, 13, 17, 19, 23, 24, 27, 29, 30, 33, 37, 39]} | 1 |
construct-nppc-vertex-cover-l4-s8 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 340 edges:
[[0, 5], [0, 9], [0, 10], [0, 14], [0, 17], [0, 19], [0, 22], [0, 27], [0, 36], [0, 37], [1, 2], [1, 5], [1, 9], [1, 10], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 21], [1, 25], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33],... | {"num_nodes": 40, "k": 20, "edges": [[0, 5], [0, 9], [0, 10], [0, 14], [0, 17], [0, 19], [0, 22], [0, 27], [0, 36], [0, 37], [1, 2], [1, 5], [1, 9], [1, 10], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 21], [1, 25], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 35], [1, 36], [1, 38], ... | null | null | null | {"cover": [1, 5, 7, 9, 10, 14, 15, 17, 18, 19, 22, 24, 26, 27, 28, 33, 35, 36, 37, 38]} | 1 |
construct-nppc-vertex-cover-l4-s9 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 4 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 40 vertices labelled 0..39 and 350 edges:
[[0, 2], [0, 3], [0, 6], [0, 8], [0, 17], [0, 31], [0, 32], [0, 35], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 17], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 27], [1, 28], [1, 29], [1, 30], [1, 32], [1, 33], [1, 3... | {"num_nodes": 40, "k": 20, "edges": [[0, 2], [0, 3], [0, 6], [0, 8], [0, 17], [0, 31], [0, 32], [0, 35], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 17], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 27], [1, 28], [1, 29], [1, 30], [1, 32], [1, 33], [1, 35], [1, 36], [1, 37], [1, 38... | null | null | null | {"cover": [1, 2, 3, 4, 6, 8, 15, 17, 18, 21, 22, 23, 25, 26, 27, 31, 32, 34, 35, 39]} | 1 |
construct-nppc-vertex-cover-l5-s0 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1409 edges:
[[0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 15], [0, 18], [0, 19], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [0, 40], [0, 42], ... | {"num_nodes": 80, "k": 40, "edges": [[0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 12], [0, 13], [0, 15], [0, 18], [0, 19], [0, 22], [0, 23], [0, 24], [0, 27], [0, 28], [0, 29], [0, 30], [0, 31], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [0, 40], [0, 42], [0, 43], [0, 44], [0, 45], [0... | null | null | null | {"cover": [0, 1, 5, 7, 11, 13, 14, 15, 16, 21, 22, 23, 24, 29, 31, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 51, 52, 53, 55, 57, 60, 61, 65, 66, 70, 71, 73, 74, 77, 78]} | 1 |
construct-nppc-vertex-cover-l5-s1 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1436 edges:
[[0, 2], [0, 5], [0, 7], [0, 8], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 33], [0, 35], [0, 38], [0, 39], [0, 40], [0, 41], [0, 42], [0, 43], [0, 45], [0, 46], [0, 47... | {"num_nodes": 80, "k": 40, "edges": [[0, 2], [0, 5], [0, 7], [0, 8], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 26], [0, 27], [0, 28], [0, 29], [0, 30], [0, 33], [0, 35], [0, 38], [0, 39], [0, 40], [0, 41], [0, 42], [0, 43], [0, 45], [0, 46], [0, 47], [0, 48], [0, 51], [0, 52],... | null | null | null | {"cover": [0, 1, 3, 4, 5, 8, 9, 10, 15, 16, 17, 18, 20, 21, 29, 32, 35, 36, 37, 38, 42, 43, 47, 48, 51, 52, 56, 59, 62, 65, 66, 68, 69, 70, 71, 72, 74, 75, 78, 79]} | 1 |
construct-nppc-vertex-cover-l5-s2 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1433 edges:
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 14], [0, 15], [0, 17], [0, 18], [0, 19], [0, 24], [0, 25], [0, 31], [0, 34], [0, 35], [0, 39], [0, 40], [0, 42], [0, 45], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [... | {"num_nodes": 80, "k": 40, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 14], [0, 15], [0, 17], [0, 18], [0, 19], [0, 24], [0, 25], [0, 31], [0, 34], [0, 35], [0, 39], [0, 40], [0, 42], [0, 45], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [0, 54], [0,... | null | null | null | {"cover": [0, 1, 2, 3, 7, 10, 12, 13, 16, 17, 18, 19, 20, 21, 25, 27, 31, 35, 39, 46, 47, 48, 49, 50, 51, 52, 53, 58, 60, 61, 62, 65, 66, 68, 70, 71, 72, 73, 75, 77]} | 1 |
construct-nppc-vertex-cover-l5-s3 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1373 edges:
[[0, 14], [0, 18], [0, 24], [0, 25], [0, 28], [0, 31], [0, 32], [0, 33], [0, 40], [0, 42], [0, 44], [0, 50], [0, 63], [0, 71], [1, 2], [1, 4], [1, 5], [1, 7], [1, 11], [1, 15], [1, 21], [1, 24], [1, 28], [1, 38], [1, 40], [1, 41], [1, 42], [1, 44], [1, 46... | {"num_nodes": 80, "k": 40, "edges": [[0, 14], [0, 18], [0, 24], [0, 25], [0, 28], [0, 31], [0, 32], [0, 33], [0, 40], [0, 42], [0, 44], [0, 50], [0, 63], [0, 71], [1, 2], [1, 4], [1, 5], [1, 7], [1, 11], [1, 15], [1, 21], [1, 24], [1, 28], [1, 38], [1, 40], [1, 41], [1, 42], [1, 44], [1, 46], [1, 49], [1, 50], [1, 51],... | null | null | null | {"cover": [2, 4, 5, 7, 11, 12, 14, 15, 18, 21, 24, 25, 28, 30, 31, 32, 33, 34, 38, 40, 41, 42, 44, 46, 48, 49, 50, 51, 54, 55, 56, 58, 60, 61, 63, 64, 66, 71, 72, 79]} | 1 |
construct-nppc-vertex-cover-l5-s4 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1409 edges:
[[0, 1], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 28], [0, 30], [0, 33], [0, 35], [0, 37], [0, 40], [0, 42], [0, 46], [0, 48], [0, 50], [0, 51],... | {"num_nodes": 80, "k": 40, "edges": [[0, 1], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 28], [0, 30], [0, 33], [0, 35], [0, 37], [0, 40], [0, 42], [0, 46], [0, 48], [0, 50], [0, 51], [0, 52], [0, 53], [0, 54], [... | null | null | null | {"cover": [0, 1, 4, 5, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 30, 35, 36, 37, 39, 40, 43, 46, 47, 51, 52, 53, 54, 60, 61, 62, 63, 65, 68, 72, 74, 76, 77, 78]} | 1 |
construct-nppc-vertex-cover-l5-s5 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1365 edges:
[[0, 1], [0, 3], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 18], [0, 19], [0, 20], [0, 23], [0, 24], [0, 25], [0, 31], [0, 33], [0, 34], [0, 35], [0, 39], [0, 40], [0, 41], [0, 44], [0, 46], [0, 47], [0, 50], [0, 52]... | {"num_nodes": 80, "k": 40, "edges": [[0, 1], [0, 3], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 18], [0, 19], [0, 20], [0, 23], [0, 24], [0, 25], [0, 31], [0, 33], [0, 34], [0, 35], [0, 39], [0, 40], [0, 41], [0, 44], [0, 46], [0, 47], [0, 50], [0, 52], [0, 55], [0, 57], [0, 58], ... | null | null | null | {"cover": [0, 1, 3, 12, 13, 15, 19, 20, 21, 23, 27, 28, 30, 31, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 49, 51, 53, 54, 55, 62, 64, 66, 67, 68, 69, 72, 74, 75, 76, 78]} | 1 |
construct-nppc-vertex-cover-l5-s6 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1393 edges:
[[0, 1], [0, 4], [0, 5], [0, 12], [0, 16], [0, 21], [0, 32], [0, 34], [0, 42], [0, 45], [0, 50], [0, 51], [0, 55], [0, 62], [0, 63], [0, 65], [0, 69], [0, 72], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 13], [1, 14], [1, 15], [1, 18], [1... | {"num_nodes": 80, "k": 40, "edges": [[0, 1], [0, 4], [0, 5], [0, 12], [0, 16], [0, 21], [0, 32], [0, 34], [0, 42], [0, 45], [0, 50], [0, 51], [0, 55], [0, 62], [0, 63], [0, 65], [0, 69], [0, 72], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 13], [1, 14], [1, 15], [1, 18], [1, 19], [1, 20], [1, 21], [1, ... | null | null | null | {"cover": [1, 4, 5, 8, 9, 12, 13, 14, 16, 18, 21, 23, 27, 32, 34, 36, 38, 41, 42, 44, 45, 46, 50, 51, 52, 55, 56, 57, 62, 63, 64, 65, 67, 68, 69, 70, 72, 74, 75, 77]} | 1 |
construct-nppc-vertex-cover-l5-s7 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1379 edges:
[[0, 6], [0, 14], [0, 15], [0, 18], [0, 20], [0, 26], [0, 28], [0, 29], [0, 38], [0, 41], [0, 44], [0, 47], [0, 49], [0, 50], [0, 52], [0, 57], [0, 60], [0, 62], [0, 63], [0, 72], [1, 6], [1, 8], [1, 9], [1, 16], [1, 20], [1, 22], [1, 24], [1, 26], [1, 29... | {"num_nodes": 80, "k": 40, "edges": [[0, 6], [0, 14], [0, 15], [0, 18], [0, 20], [0, 26], [0, 28], [0, 29], [0, 38], [0, 41], [0, 44], [0, 47], [0, 49], [0, 50], [0, 52], [0, 57], [0, 60], [0, 62], [0, 63], [0, 72], [1, 6], [1, 8], [1, 9], [1, 16], [1, 20], [1, 22], [1, 24], [1, 26], [1, 29], [1, 31], [1, 38], [1, 47],... | null | null | null | {"cover": [2, 4, 6, 8, 9, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 29, 31, 38, 41, 44, 45, 47, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 68, 72, 73, 74, 77, 78]} | 1 |
construct-nppc-vertex-cover-l5-s8 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1431 edges:
[[0, 2], [0, 5], [0, 6], [0, 14], [0, 21], [0, 23], [0, 28], [0, 38], [0, 40], [0, 51], [0, 59], [0, 63], [0, 66], [0, 68], [0, 69], [0, 70], [0, 72], [1, 3], [1, 9], [1, 10], [1, 22], [1, 23], [1, 25], [1, 28], [1, 47], [1, 49], [1, 59], [1, 66], [1, 67]... | {"num_nodes": 80, "k": 40, "edges": [[0, 2], [0, 5], [0, 6], [0, 14], [0, 21], [0, 23], [0, 28], [0, 38], [0, 40], [0, 51], [0, 59], [0, 63], [0, 66], [0, 68], [0, 69], [0, 70], [0, 72], [1, 3], [1, 9], [1, 10], [1, 22], [1, 23], [1, 25], [1, 28], [1, 47], [1, 49], [1, 59], [1, 66], [1, 67], [1, 68], [1, 69], [1, 71], ... | null | null | null | {"cover": [2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 21, 22, 23, 25, 27, 28, 30, 33, 37, 38, 39, 40, 43, 47, 49, 50, 51, 59, 63, 66, 67, 68, 69, 70, 71, 72, 74, 75, 78, 79]} | 1 |
construct-nppc-vertex-cover-l5-s9 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 5 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 80 vertices labelled 0..79 and 1415 edges:
[[0, 5], [0, 8], [0, 9], [0, 19], [0, 21], [0, 37], [0, 40], [0, 41], [0, 46], [0, 49], [0, 50], [0, 53], [0, 58], [0, 61], [0, 64], [0, 67], [0, 71], [0, 76], [0, 77], [1, 4], [1, 5], [1, 6], [1, 7], [1, 9], [1, 11], [1, 12], [1, 17], [1, 18], [1, 19], [... | {"num_nodes": 80, "k": 40, "edges": [[0, 5], [0, 8], [0, 9], [0, 19], [0, 21], [0, 37], [0, 40], [0, 41], [0, 46], [0, 49], [0, 50], [0, 53], [0, 58], [0, 61], [0, 64], [0, 67], [0, 71], [0, 76], [0, 77], [1, 4], [1, 5], [1, 6], [1, 7], [1, 9], [1, 11], [1, 12], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1,... | null | null | null | {"cover": [1, 5, 7, 8, 9, 12, 13, 16, 18, 19, 21, 22, 24, 29, 30, 31, 35, 36, 37, 40, 41, 43, 45, 46, 49, 50, 53, 54, 56, 58, 59, 61, 64, 67, 69, 71, 72, 76, 77, 79]} | 1 |
construct-nppc-vertex-cover-l6-s0 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1621 edges:
[[0, 8], [0, 10], [0, 14], [0, 18], [0, 27], [0, 29], [0, 133], [0, 137], [1, 4], [1, 13], [1, 18], [1, 70], [1, 71], [1, 129], [2, 9], [2, 25], [2, 28], [2, 35], [2, 39], [2, 41], [2, 42], [2, 50], [2, 53], [2, 56], [2, 62], [2, 66], [2, 74], [2, 75], ... | {"num_nodes": 160, "k": 64, "edges": [[0, 8], [0, 10], [0, 14], [0, 18], [0, 27], [0, 29], [0, 133], [0, 137], [1, 4], [1, 13], [1, 18], [1, 70], [1, 71], [1, 129], [2, 9], [2, 25], [2, 28], [2, 35], [2, 39], [2, 41], [2, 42], [2, 50], [2, 53], [2, 56], [2, 62], [2, 66], [2, 74], [2, 75], [2, 89], [2, 91], [2, 101], [2... | null | null | null | {"cover": [2, 3, 4, 6, 8, 9, 10, 11, 13, 14, 18, 19, 20, 21, 24, 26, 27, 28, 29, 34, 35, 36, 37, 40, 42, 45, 48, 53, 57, 59, 62, 64, 69, 70, 71, 75, 83, 85, 86, 93, 94, 96, 100, 101, 106, 107, 111, 113, 115, 117, 119, 122, 129, 131, 132, 133, 134, 135, 137, 147, 151, 152, 157, 159]} | 1 |
construct-nppc-vertex-cover-l6-s1 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1535 edges:
[[0, 3], [0, 4], [0, 8], [0, 17], [0, 22], [0, 25], [0, 50], [0, 56], [0, 59], [0, 80], [0, 83], [0, 84], [0, 86], [0, 89], [0, 91], [0, 108], [0, 109], [0, 113], [0, 124], [0, 130], [0, 131], [0, 134], [0, 155], [1, 6], [1, 7], [1, 15], [1, 19], [1, 31... | {"num_nodes": 160, "k": 64, "edges": [[0, 3], [0, 4], [0, 8], [0, 17], [0, 22], [0, 25], [0, 50], [0, 56], [0, 59], [0, 80], [0, 83], [0, 84], [0, 86], [0, 89], [0, 91], [0, 108], [0, 109], [0, 113], [0, 124], [0, 130], [0, 131], [0, 134], [0, 155], [1, 6], [1, 7], [1, 15], [1, 19], [1, 31], [1, 32], [1, 39], [1, 40], ... | null | null | null | {"cover": [0, 1, 10, 16, 20, 22, 23, 25, 27, 28, 29, 31, 32, 33, 35, 36, 41, 42, 45, 50, 52, 53, 62, 65, 66, 69, 73, 74, 75, 76, 78, 81, 83, 84, 88, 90, 91, 93, 99, 103, 106, 107, 108, 109, 111, 112, 113, 114, 116, 121, 122, 126, 129, 133, 136, 137, 139, 145, 148, 149, 150, 151, 153, 156]} | 1 |
construct-nppc-vertex-cover-l6-s2 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1515 edges:
[[0, 108], [0, 125], [0, 127], [0, 137], [0, 147], [0, 158], [1, 20], [1, 71], [1, 96], [1, 124], [1, 128], [1, 136], [1, 137], [1, 153], [2, 6], [2, 7], [2, 15], [2, 18], [2, 24], [2, 27], [2, 32], [2, 45], [2, 49], [2, 57], [2, 63], [2, 64], [2, 66], ... | {"num_nodes": 160, "k": 64, "edges": [[0, 108], [0, 125], [0, 127], [0, 137], [0, 147], [0, 158], [1, 20], [1, 71], [1, 96], [1, 124], [1, 128], [1, 136], [1, 137], [1, 153], [2, 6], [2, 7], [2, 15], [2, 18], [2, 24], [2, 27], [2, 32], [2, 45], [2, 49], [2, 57], [2, 63], [2, 64], [2, 66], [2, 68], [2, 73], [2, 74], [2,... | null | null | null | {"cover": [2, 6, 7, 9, 12, 15, 19, 20, 21, 23, 27, 28, 36, 38, 39, 40, 41, 46, 49, 52, 53, 66, 67, 68, 69, 71, 74, 77, 80, 85, 88, 91, 94, 95, 96, 98, 99, 101, 102, 103, 104, 106, 108, 113, 120, 124, 125, 127, 128, 130, 132, 135, 136, 137, 138, 141, 145, 147, 148, 150, 152, 153, 158, 159]} | 1 |
construct-nppc-vertex-cover-l6-s3 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1574 edges:
[[0, 6], [0, 7], [0, 13], [0, 46], [0, 50], [0, 59], [0, 61], [0, 73], [0, 84], [0, 87], [0, 99], [0, 104], [0, 107], [0, 120], [0, 127], [0, 150], [1, 6], [1, 13], [1, 14], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 24], [1, 29], [1, 33], [1, 35]... | {"num_nodes": 160, "k": 64, "edges": [[0, 6], [0, 7], [0, 13], [0, 46], [0, 50], [0, 59], [0, 61], [0, 73], [0, 84], [0, 87], [0, 99], [0, 104], [0, 107], [0, 120], [0, 127], [0, 150], [1, 6], [1, 13], [1, 14], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 24], [1, 29], [1, 33], [1, 35], [1, 37], [1, 38], [1, 46], [... | null | null | null | {"cover": [1, 3, 6, 7, 8, 11, 13, 21, 23, 24, 28, 30, 32, 33, 40, 44, 45, 46, 50, 51, 55, 59, 61, 65, 67, 71, 73, 75, 78, 79, 80, 84, 86, 87, 88, 89, 95, 99, 100, 102, 104, 107, 108, 110, 111, 114, 115, 118, 120, 121, 127, 129, 130, 133, 137, 138, 139, 141, 143, 144, 146, 147, 150, 156]} | 1 |
construct-nppc-vertex-cover-l6-s4 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1586 edges:
[[0, 38], [0, 51], [0, 81], [0, 121], [0, 133], [0, 139], [1, 6], [1, 11], [1, 14], [1, 15], [1, 18], [1, 19], [1, 23], [1, 29], [1, 30], [1, 33], [1, 39], [1, 40], [1, 47], [1, 57], [1, 60], [1, 62], [1, 68], [1, 69], [1, 72], [1, 79], [1, 87], [1, 97]... | {"num_nodes": 160, "k": 64, "edges": [[0, 38], [0, 51], [0, 81], [0, 121], [0, 133], [0, 139], [1, 6], [1, 11], [1, 14], [1, 15], [1, 18], [1, 19], [1, 23], [1, 29], [1, 30], [1, 33], [1, 39], [1, 40], [1, 47], [1, 57], [1, 60], [1, 62], [1, 68], [1, 69], [1, 72], [1, 79], [1, 87], [1, 97], [1, 108], [1, 110], [1, 121]... | null | null | null | {"cover": [1, 3, 6, 8, 9, 14, 15, 18, 19, 20, 21, 23, 24, 26, 29, 30, 33, 38, 40, 43, 44, 47, 50, 51, 53, 54, 55, 56, 57, 58, 62, 64, 69, 80, 81, 82, 88, 89, 93, 95, 98, 100, 109, 110, 113, 115, 116, 119, 120, 121, 123, 126, 129, 133, 137, 139, 142, 144, 145, 148, 150, 155, 157, 158]} | 1 |
construct-nppc-vertex-cover-l6-s5 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1591 edges:
[[0, 4], [0, 5], [0, 18], [0, 19], [0, 23], [0, 28], [0, 33], [0, 35], [0, 36], [0, 41], [0, 44], [0, 47], [0, 50], [0, 62], [0, 63], [0, 72], [0, 74], [0, 80], [0, 81], [0, 86], [0, 90], [0, 106], [0, 107], [0, 115], [0, 116], [0, 119], [0, 126], [0, 1... | {"num_nodes": 160, "k": 64, "edges": [[0, 4], [0, 5], [0, 18], [0, 19], [0, 23], [0, 28], [0, 33], [0, 35], [0, 36], [0, 41], [0, 44], [0, 47], [0, 50], [0, 62], [0, 63], [0, 72], [0, 74], [0, 80], [0, 81], [0, 86], [0, 90], [0, 106], [0, 107], [0, 115], [0, 116], [0, 119], [0, 126], [0, 128], [0, 132], [0, 135], [0, 1... | null | null | null | {"cover": [0, 3, 5, 13, 15, 16, 17, 23, 25, 26, 27, 30, 35, 39, 44, 49, 52, 58, 61, 63, 65, 67, 69, 72, 73, 74, 77, 80, 83, 84, 88, 91, 92, 96, 97, 100, 102, 103, 104, 105, 112, 114, 115, 118, 119, 121, 127, 128, 129, 130, 132, 133, 136, 137, 138, 139, 141, 143, 148, 149, 152, 153, 154, 156]} | 1 |
construct-nppc-vertex-cover-l6-s6 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1538 edges:
[[0, 6], [0, 18], [0, 20], [0, 65], [0, 101], [0, 138], [0, 142], [0, 150], [0, 154], [1, 7], [1, 9], [1, 10], [1, 15], [1, 20], [1, 28], [1, 29], [1, 31], [1, 32], [1, 50], [1, 51], [1, 56], [1, 59], [1, 63], [1, 64], [1, 72], [1, 88], [1, 92], [1, 105... | {"num_nodes": 160, "k": 64, "edges": [[0, 6], [0, 18], [0, 20], [0, 65], [0, 101], [0, 138], [0, 142], [0, 150], [0, 154], [1, 7], [1, 9], [1, 10], [1, 15], [1, 20], [1, 28], [1, 29], [1, 31], [1, 32], [1, 50], [1, 51], [1, 56], [1, 59], [1, 63], [1, 64], [1, 72], [1, 88], [1, 92], [1, 105], [1, 107], [1, 110], [1, 118... | null | null | null | {"cover": [1, 2, 3, 6, 9, 18, 20, 21, 24, 25, 28, 29, 38, 42, 43, 51, 52, 54, 58, 60, 65, 68, 69, 70, 71, 74, 80, 85, 87, 98, 99, 101, 102, 103, 105, 107, 109, 111, 114, 117, 118, 119, 120, 125, 126, 129, 130, 133, 134, 136, 137, 138, 139, 140, 142, 144, 146, 147, 148, 150, 152, 153, 154, 159]} | 1 |
construct-nppc-vertex-cover-l6-s7 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1564 edges:
[[0, 68], [0, 148], [0, 152], [1, 15], [1, 24], [1, 33], [1, 47], [1, 52], [1, 70], [1, 75], [1, 76], [1, 79], [1, 142], [1, 159], [2, 4], [2, 5], [2, 8], [2, 10], [2, 14], [2, 16], [2, 17], [2, 21], [2, 33], [2, 40], [2, 41], [2, 45], [2, 52], [2, 53],... | {"num_nodes": 160, "k": 64, "edges": [[0, 68], [0, 148], [0, 152], [1, 15], [1, 24], [1, 33], [1, 47], [1, 52], [1, 70], [1, 75], [1, 76], [1, 79], [1, 142], [1, 159], [2, 4], [2, 5], [2, 8], [2, 10], [2, 14], [2, 16], [2, 17], [2, 21], [2, 33], [2, 40], [2, 41], [2, 45], [2, 52], [2, 53], [2, 55], [2, 62], [2, 65], [2... | null | null | null | {"cover": [2, 3, 9, 13, 15, 16, 19, 21, 23, 24, 33, 34, 41, 42, 45, 47, 50, 52, 53, 56, 62, 68, 69, 70, 71, 73, 75, 76, 78, 79, 81, 83, 87, 89, 91, 95, 96, 97, 100, 103, 104, 105, 112, 115, 116, 120, 122, 124, 125, 127, 128, 130, 134, 137, 139, 141, 142, 145, 148, 150, 152, 156, 157, 159]} | 1 |
construct-nppc-vertex-cover-l6-s8 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1630 edges:
[[0, 6], [0, 18], [0, 23], [0, 50], [0, 63], [0, 66], [0, 90], [0, 96], [0, 108], [0, 122], [0, 124], [0, 142], [0, 147], [1, 6], [1, 8], [1, 9], [1, 11], [1, 12], [1, 15], [1, 23], [1, 26], [1, 34], [1, 38], [1, 49], [1, 54], [1, 55], [1, 57], [1, 58],... | {"num_nodes": 160, "k": 64, "edges": [[0, 6], [0, 18], [0, 23], [0, 50], [0, 63], [0, 66], [0, 90], [0, 96], [0, 108], [0, 122], [0, 124], [0, 142], [0, 147], [1, 6], [1, 8], [1, 9], [1, 11], [1, 12], [1, 15], [1, 23], [1, 26], [1, 34], [1, 38], [1, 49], [1, 54], [1, 55], [1, 57], [1, 58], [1, 61], [1, 64], [1, 65], [1... | null | null | null | {"cover": [1, 4, 6, 10, 11, 13, 14, 15, 16, 18, 19, 21, 23, 30, 31, 39, 41, 43, 46, 47, 50, 52, 55, 57, 58, 59, 61, 63, 65, 66, 68, 73, 75, 79, 81, 85, 88, 90, 91, 93, 94, 95, 96, 98, 99, 102, 106, 108, 110, 113, 115, 118, 121, 122, 124, 127, 136, 139, 142, 143, 147, 149, 155, 159]} | 1 |
construct-nppc-vertex-cover-l6-s9 | construct | nppc_vertex_cover | graph_vertex_cover | graph_theory | competition | 6 | NPPC/vertex_cover | MIT | [
"agentic_trivial",
"np_search"
] | Undirected graph with 160 vertices labelled 0..159 and 1544 edges:
[[0, 6], [0, 12], [0, 15], [0, 23], [0, 29], [0, 55], [0, 57], [0, 59], [0, 65], [0, 67], [0, 75], [0, 83], [0, 86], [0, 90], [0, 103], [0, 105], [0, 107], [0, 108], [0, 117], [0, 119], [0, 131], [0, 133], [0, 142], [0, 145], [0, 155], [0, 156], [1, 7],... | {"num_nodes": 160, "k": 64, "edges": [[0, 6], [0, 12], [0, 15], [0, 23], [0, 29], [0, 55], [0, 57], [0, 59], [0, 65], [0, 67], [0, 75], [0, 83], [0, 86], [0, 90], [0, 103], [0, 105], [0, 107], [0, 108], [0, 117], [0, 119], [0, 131], [0, 133], [0, 142], [0, 145], [0, 155], [0, 156], [1, 7], [1, 23], [1, 33], [1, 49], [1... | null | null | null | {"cover": [0, 2, 3, 5, 6, 7, 10, 13, 20, 23, 25, 32, 33, 35, 37, 39, 40, 41, 42, 46, 47, 49, 52, 54, 55, 59, 60, 62, 65, 73, 74, 83, 89, 90, 92, 94, 96, 98, 102, 103, 104, 106, 108, 109, 111, 112, 114, 117, 124, 125, 128, 136, 138, 143, 147, 149, 150, 152, 153, 154, 155, 157, 158, 159]} | 1 |
construct-rg-graph-color-l1-s0 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 4], [1, 2], [1, 4], [2, 3], [4, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 4], [1, 2], [1, 4], [2, 3], [4, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 2, 1]} | 1 |
construct-rg-graph-color-l1-s1 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 2], [0, 4], [0, 5], [1, 5], [2, 3]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 2], [0, 4], [0, 5], [1, 5], [2, 3]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 2, 2]} | 1 |
construct-rg-graph-color-l1-s2 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 1], [0, 2], [0, 3], [0, 5], [1, 2], [1, 4]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final a... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [1, 2], [1, 4]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 3, 2, 1, 2]} | 1 |
construct-rg-graph-color-l1-s3 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 3], [0, 4], [1, 4], [1, 5], [4, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 3], [0, 4], [1, 4], [1, 5], [4, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 2, 3]} | 1 |
construct-rg-graph-color-l1-s4 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 1], [0, 2], [0, 3], [0, 4], [1, 4], [2, 4], [2, 5], [3, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Wr... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [1, 4], [2, 4], [2, 5], [3, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 2, 2, 3, 1]} | 1 |
construct-rg-graph-color-l1-s5 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 4], [1, 4], [2, 4], [2, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as JSON to... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 4], [1, 4], [2, 4], [2, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 1, 2, 2]} | 1 |
construct-rg-graph-color-l1-s6 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 1], [1, 4], [2, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as JSON to `/workd... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 1], [1, 4], [2, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 1, 1, 1, 2]} | 1 |
construct-rg-graph-color-l1-s7 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 3], [0, 4], [1, 3], [3, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as JSON to... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 3], [0, 4], [1, 3], [3, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 2, 1]} | 1 |
construct-rg-graph-color-l1-s8 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 2], [0, 4], [1, 2], [1, 5], [2, 3], [3, 4]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final a... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 2], [0, 4], [1, 2], [1, 5], [2, 3], [3, 4]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 2, 2]} | 1 |
construct-rg-graph-color-l1-s9 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 1 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5]
Edges: [[0, 4], [1, 3], [2, 4], [4, 5]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
Write your final answer as JSON to... | {"num_vertices": 6, "num_colors": 4, "edges": [[0, 4], [1, 3], [2, 4], [4, 5]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 2, 1]} | 1 |
construct-rg-graph-color-l2-s0 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 2], [0, 4], [0, 9], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [2, 4], [2, 5], [2, 6], [4, 5], [5, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 2], [0, 4], [0, 9], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [2, 4], [2, 5], [2, 6], [4, 5], [5, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 3, 1, 3, 2, 2, 2]} | 1 |
construct-rg-graph-color-l2-s1 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 4], [0, 6], [0, 7], [1, 2], [1, 7], [2, 8], [2, 9], [3, 8], [4, 9], [5, 6], [5, 7], [5, 8], [6, 8], [7, 8]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 4], [0, 6], [0, 7], [1, 2], [1, 7], [2, 8], [2, 9], [3, 8], [4, 9], [5, 6], [5, 7], [5, 8], [6, 8], [7, 8]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 2, 1, 2, 2, 3, 1]} | 1 |
construct-rg-graph-color-l2-s2 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 9], [1, 3], [1, 4], [1, 6], [1, 7], [1, 9], [2, 3], [2, 4], [2, 7], [2, 9], [3, 5], [3, 7], [3, 8], [3, 9], [4, 8], [5, 8], [6, 7], [6, 8], [7, 9], [8, 9]]
Possible colours: [1,... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 9], [1, 3], [1, 4], [1, 6], [1, 7], [1, 9], [2, 3], [2, 4], [2, 7], [2, 9], [3, 5], [3, 7], [3, 8], [3, 9], [4, 8], [5, 8], [6, 7], [6, 8], [7, 9], [8, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 2, 1, 2, 3, 3, 4]} | 1 |
construct-rg-graph-color-l2-s3 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 7], [0, 8], [1, 4], [2, 6], [3, 8], [5, 6], [5, 7], [8, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..4 is the co... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 1], [0, 7], [0, 8], [1, 4], [2, 6], [3, 8], [5, 6], [5, 7], [8, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 1, 1, 1, 1, 2, 2, 2, 1]} | 1 |
construct-rg-graph-color-l2-s4 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 2], [1, 2], [1, 4], [1, 9], [2, 5], [2, 8], [3, 4], [4, 7], [5, 6], [5, 7], [6, 8], [7, 8], [7, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 2], [1, 2], [1, 4], [1, 9], [2, 5], [2, 8], [3, 4], [4, 7], [5, 6], [5, 7], [6, 8], [7, 8], [7, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 2, 1, 2, 3, 1, 2]} | 1 |
construct-rg-graph-color-l2-s5 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 2], [0, 4], [0, 6], [1, 2], [1, 7], [1, 9], [2, 4], [3, 4], [3, 7], [4, 6], [5, 6], [5, 7], [6, 7], [6, 9], [7, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"colo... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 1], [0, 2], [0, 4], [0, 6], [1, 2], [1, 7], [1, 9], [2, 4], [3, 4], [3, 7], [4, 6], [5, 6], [5, 7], [6, 7], [6, 9], [7, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 3, 1, 2, 1, 3, 4, 1, 1]} | 1 |
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