task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-mc-max-clique-l6-s6 | construct | mc_max_clique | graph_clique | graph_theory | competition | 6 | MathConstraint/max_clique | CC-BY-4.0 | [
"np_search"
] | Graph G with 120 vertices numbered 0..119 and 3714 edges:
(0,2), (0,3), (0,4), (0,5), (0,6), (0,8), (0,10), (0,11), (0,12), (0,14), (0,15), (0,16), (0,17), (0,18), (0,21), (0,22), (0,24), (0,25), (0,26), (0,27), (0,28), (0,29), (0,34), (0,36), (0,37), (0,42), (0,45), (0,47), (0,50), (0,53), (0,54), (0,55), (0,58), (0,5... | {"n": 120, "k": 13, "edges": [[0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 21], [0, 22], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 34], [0, 36], [0, 37], [0, 42], [0, 45], [0, 47], [0, 50], [0, 53], [0, 54], [0, 55], [0, 58],... | null | null | null | {"clique": [7, 12, 17, 18, 31, 41, 48, 65, 68, 83, 94, 95, 108]} | 1 |
construct-mc-max-clique-l6-s7 | construct | mc_max_clique | graph_clique | graph_theory | competition | 6 | MathConstraint/max_clique | CC-BY-4.0 | [
"np_search"
] | Graph G with 120 vertices numbered 0..119 and 3602 edges:
(0,1), (0,2), (0,3), (0,6), (0,7), (0,10), (0,11), (0,12), (0,16), (0,18), (0,20), (0,21), (0,23), (0,25), (0,26), (0,27), (0,28), (0,29), (0,31), (0,33), (0,35), (0,39), (0,40), (0,45), (0,48), (0,51), (0,53), (0,54), (0,55), (0,57), (0,59), (0,64), (0,65), (0,... | {"n": 120, "k": 13, "edges": [[0, 1], [0, 2], [0, 3], [0, 6], [0, 7], [0, 10], [0, 11], [0, 12], [0, 16], [0, 18], [0, 20], [0, 21], [0, 23], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [0, 31], [0, 33], [0, 35], [0, 39], [0, 40], [0, 45], [0, 48], [0, 51], [0, 53], [0, 54], [0, 55], [0, 57], [0, 59], [0, 64], [0, 65]... | null | null | null | {"clique": [11, 16, 24, 36, 53, 63, 67, 74, 75, 78, 81, 82, 118]} | 1 |
construct-mc-max-clique-l6-s8 | construct | mc_max_clique | graph_clique | graph_theory | competition | 6 | MathConstraint/max_clique | CC-BY-4.0 | [
"np_search"
] | Graph G with 120 vertices numbered 0..119 and 3635 edges:
(0,2), (0,4), (0,6), (0,9), (0,11), (0,12), (0,19), (0,21), (0,23), (0,24), (0,26), (0,28), (0,30), (0,31), (0,32), (0,33), (0,36), (0,37), (0,38), (0,39), (0,40), (0,41), (0,43), (0,48), (0,50), (0,51), (0,52), (0,53), (0,56), (0,58), (0,60), (0,61), (0,62), (0... | {"n": 120, "k": 13, "edges": [[0, 2], [0, 4], [0, 6], [0, 9], [0, 11], [0, 12], [0, 19], [0, 21], [0, 23], [0, 24], [0, 26], [0, 28], [0, 30], [0, 31], [0, 32], [0, 33], [0, 36], [0, 37], [0, 38], [0, 39], [0, 40], [0, 41], [0, 43], [0, 48], [0, 50], [0, 51], [0, 52], [0, 53], [0, 56], [0, 58], [0, 60], [0, 61], [0, 62... | null | null | null | {"clique": [4, 18, 37, 42, 43, 44, 47, 52, 75, 81, 85, 87, 94]} | 1 |
construct-mc-max-clique-l6-s9 | construct | mc_max_clique | graph_clique | graph_theory | competition | 6 | MathConstraint/max_clique | CC-BY-4.0 | [
"np_search"
] | Graph G with 120 vertices numbered 0..119 and 3632 edges:
(0,2), (0,4), (0,6), (0,7), (0,8), (0,9), (0,10), (0,13), (0,14), (0,16), (0,17), (0,20), (0,21), (0,24), (0,27), (0,29), (0,30), (0,35), (0,38), (0,39), (0,40), (0,42), (0,43), (0,44), (0,45), (0,46), (0,47), (0,48), (0,49), (0,50), (0,51), (0,54), (0,56), (0,5... | {"n": 120, "k": 13, "edges": [[0, 2], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 13], [0, 14], [0, 16], [0, 17], [0, 20], [0, 21], [0, 24], [0, 27], [0, 29], [0, 30], [0, 35], [0, 38], [0, 39], [0, 40], [0, 42], [0, 43], [0, 44], [0, 45], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 54], [0, 56],... | null | null | null | {"clique": [2, 17, 23, 40, 49, 53, 61, 65, 83, 88, 101, 111, 115]} | 1 |
construct-mc-max-independent-set-l1-s0 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 54 edges:
(0,1), (0,4), (0,8), (0,11), (0,16), (1,7), (1,13), (1,17), (1,19), (2,3), (2,4), (2,9), (2,11), (2,14), (2,17), (3,4), (3,8), (3,16), (4,11), (4,13), (4,16), (5,10), (5,11), (5,14), (5,19), (6,9), (6,11), (6,12), (6,15), (8,11), (8,16), (9,11), (9,12), (9,13), (9,1... | {"n": 20, "k": 7, "edges": [[0, 1], [0, 4], [0, 8], [0, 11], [0, 16], [1, 7], [1, 13], [1, 17], [1, 19], [2, 3], [2, 4], [2, 9], [2, 11], [2, 14], [2, 17], [3, 4], [3, 8], [3, 16], [4, 11], [4, 13], [4, 16], [5, 10], [5, 11], [5, 14], [5, 19], [6, 9], [6, 11], [6, 12], [6, 15], [8, 11], [8, 16], [9, 11], [9, 12], [9, 1... | null | null | null | {"independent_set": [0, 3, 5, 7, 15, 17, 18]} | 1 |
construct-mc-max-independent-set-l1-s1 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 42 edges:
(0,4), (1,3), (1,7), (1,15), (1,16), (1,19), (2,6), (2,8), (2,10), (2,15), (3,5), (3,9), (3,11), (3,19), (4,9), (4,10), (4,14), (4,17), (4,19), (5,11), (5,12), (5,14), (7,11), (7,13), (7,14), (7,18), (8,13), (8,16), (9,11), (10,11), (10,16), (11,17), (11,19), (12,13... | {"n": 20, "k": 7, "edges": [[0, 4], [1, 3], [1, 7], [1, 15], [1, 16], [1, 19], [2, 6], [2, 8], [2, 10], [2, 15], [3, 5], [3, 9], [3, 11], [3, 19], [4, 9], [4, 10], [4, 14], [4, 17], [4, 19], [5, 11], [5, 12], [5, 14], [7, 11], [7, 13], [7, 14], [7, 18], [8, 13], [8, 16], [9, 11], [10, 11], [10, 16], [11, 17], [11, 19],... | null | null | null | {"independent_set": [0, 6, 8, 9, 12, 14, 15]} | 1 |
construct-mc-max-independent-set-l1-s2 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 49 edges:
(0,4), (0,6), (0,12), (0,18), (1,9), (1,10), (1,13), (2,3), (2,4), (2,5), (2,12), (2,15), (2,16), (3,5), (3,6), (3,18), (4,5), (4,6), (4,7), (4,16), (4,17), (5,8), (5,10), (5,13), (5,17), (6,15), (6,16), (7,12), (7,19), (8,14), (8,19), (9,17), (10,11), (10,12), (10,... | {"n": 20, "k": 7, "edges": [[0, 4], [0, 6], [0, 12], [0, 18], [1, 9], [1, 10], [1, 13], [2, 3], [2, 4], [2, 5], [2, 12], [2, 15], [2, 16], [3, 5], [3, 6], [3, 18], [4, 5], [4, 6], [4, 7], [4, 16], [4, 17], [5, 8], [5, 10], [5, 13], [5, 17], [6, 15], [6, 16], [7, 12], [7, 19], [8, 14], [8, 19], [9, 17], [10, 11], [10, 1... | null | null | null | {"independent_set": [2, 6, 7, 9, 10, 13, 18]} | 1 |
construct-mc-max-independent-set-l1-s3 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 58 edges:
(0,8), (0,9), (0,16), (0,17), (1,5), (1,9), (1,10), (1,15), (1,17), (2,8), (2,9), (2,10), (3,5), (3,6), (3,8), (3,11), (3,13), (3,15), (4,5), (4,6), (4,19), (5,7), (5,9), (5,16), (5,18), (6,11), (6,13), (7,9), (7,11), (7,13), (7,14), (7,17), (7,19), (8,11), (8,12), ... | {"n": 20, "k": 7, "edges": [[0, 8], [0, 9], [0, 16], [0, 17], [1, 5], [1, 9], [1, 10], [1, 15], [1, 17], [2, 8], [2, 9], [2, 10], [3, 5], [3, 6], [3, 8], [3, 11], [3, 13], [3, 15], [4, 5], [4, 6], [4, 19], [5, 7], [5, 9], [5, 16], [5, 18], [6, 11], [6, 13], [7, 9], [7, 11], [7, 13], [7, 14], [7, 17], [7, 19], [8, 11], ... | null | null | null | {"independent_set": [0, 2, 4, 7, 12, 15, 18]} | 1 |
construct-mc-max-independent-set-l1-s4 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 43 edges:
(0,5), (0,7), (0,10), (0,11), (0,12), (0,15), (1,6), (1,9), (1,14), (1,16), (2,6), (2,18), (3,8), (3,14), (3,15), (3,17), (3,19), (4,5), (4,7), (4,11), (4,16), (5,8), (5,9), (5,12), (5,17), (6,9), (6,12), (6,17), (6,18), (6,19), (7,10), (7,15), (7,18), (8,13), (8,16... | {"n": 20, "k": 7, "edges": [[0, 5], [0, 7], [0, 10], [0, 11], [0, 12], [0, 15], [1, 6], [1, 9], [1, 14], [1, 16], [2, 6], [2, 18], [3, 8], [3, 14], [3, 15], [3, 17], [3, 19], [4, 5], [4, 7], [4, 11], [4, 16], [5, 8], [5, 9], [5, 12], [5, 17], [6, 9], [6, 12], [6, 17], [6, 18], [6, 19], [7, 10], [7, 15], [7, 18], [8, 13... | null | null | null | {"independent_set": [2, 7, 8, 12, 14, 17, 19]} | 1 |
construct-mc-max-independent-set-l1-s5 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 42 edges:
(0,3), (0,4), (0,6), (0,7), (0,8), (0,9), (0,10), (0,11), (0,12), (0,14), (0,18), (1,2), (1,3), (1,5), (1,19), (2,7), (2,15), (3,5), (3,9), (3,11), (3,15), (3,18), (3,19), (4,7), (4,8), (5,9), (6,12), (6,13), (7,9), (7,12), (7,14), (7,18), (9,13), (9,19), (10,13), (... | {"n": 20, "k": 7, "edges": [[0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 14], [0, 18], [1, 2], [1, 3], [1, 5], [1, 19], [2, 7], [2, 15], [3, 5], [3, 9], [3, 11], [3, 15], [3, 18], [3, 19], [4, 7], [4, 8], [5, 9], [6, 12], [6, 13], [7, 9], [7, 12], [7, 14], [7, 18], [9, 13], [9, 19], [1... | null | null | null | {"independent_set": [4, 5, 6, 10, 14, 17, 18]} | 1 |
construct-mc-max-independent-set-l1-s6 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 61 edges:
(0,1), (0,3), (0,5), (0,7), (0,8), (0,9), (0,10), (0,13), (0,17), (1,2), (1,5), (1,11), (1,13), (1,15), (1,17), (1,18), (2,10), (2,14), (2,17), (3,5), (3,6), (3,9), (3,10), (3,15), (3,19), (4,5), (4,6), (4,10), (4,14), (4,18), (5,6), (5,9), (5,10), (5,15), (5,17), (... | {"n": 20, "k": 7, "edges": [[0, 1], [0, 3], [0, 5], [0, 7], [0, 8], [0, 9], [0, 10], [0, 13], [0, 17], [1, 2], [1, 5], [1, 11], [1, 13], [1, 15], [1, 17], [1, 18], [2, 10], [2, 14], [2, 17], [3, 5], [3, 6], [3, 9], [3, 10], [3, 15], [3, 19], [4, 5], [4, 6], [4, 10], [4, 14], [4, 18], [5, 6], [5, 9], [5, 10], [5, 15], [... | null | null | null | {"independent_set": [2, 3, 4, 7, 12, 13, 16]} | 1 |
construct-mc-max-independent-set-l1-s7 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 48 edges:
(0,8), (1,6), (1,7), (1,9), (1,11), (1,13), (1,16), (2,4), (2,5), (2,10), (2,18), (3,6), (3,8), (3,16), (3,19), (4,9), (4,10), (4,19), (5,9), (5,10), (5,11), (5,13), (5,16), (5,17), (6,7), (6,12), (6,14), (6,17), (7,19), (8,10), (8,12), (8,16), (8,17), (9,11), (9,16... | {"n": 20, "k": 7, "edges": [[0, 8], [1, 6], [1, 7], [1, 9], [1, 11], [1, 13], [1, 16], [2, 4], [2, 5], [2, 10], [2, 18], [3, 6], [3, 8], [3, 16], [3, 19], [4, 9], [4, 10], [4, 19], [5, 9], [5, 10], [5, 11], [5, 13], [5, 16], [5, 17], [6, 7], [6, 12], [6, 14], [6, 17], [7, 19], [8, 10], [8, 12], [8, 16], [8, 17], [9, 11... | null | null | null | {"independent_set": [2, 3, 7, 11, 12, 13, 14]} | 1 |
construct-mc-max-independent-set-l1-s8 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 56 edges:
(0,12), (0,13), (0,15), (0,16), (0,17), (0,19), (1,5), (1,7), (1,8), (1,15), (1,16), (2,3), (2,5), (2,7), (2,8), (2,11), (2,12), (2,14), (2,15), (2,17), (3,10), (3,17), (4,12), (4,13), (4,14), (4,16), (5,8), (5,11), (6,12), (6,17), (7,9), (7,14), (7,15), (7,16), (7,... | {"n": 20, "k": 7, "edges": [[0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [1, 5], [1, 7], [1, 8], [1, 15], [1, 16], [2, 3], [2, 5], [2, 7], [2, 8], [2, 11], [2, 12], [2, 14], [2, 15], [2, 17], [3, 10], [3, 17], [4, 12], [4, 13], [4, 14], [4, 16], [5, 8], [5, 11], [6, 12], [6, 17], [7, 9], [7, 14], [7, 15], [7, ... | null | null | null | {"independent_set": [0, 1, 2, 4, 6, 9, 10]} | 1 |
construct-mc-max-independent-set-l1-s9 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 1 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 49 edges:
(0,5), (0,6), (0,9), (0,18), (1,5), (1,16), (1,17), (1,19), (2,7), (2,9), (2,10), (2,13), (2,15), (2,17), (3,9), (3,10), (4,9), (4,11), (4,12), (4,14), (4,15), (4,16), (4,17), (5,6), (6,9), (6,12), (6,15), (7,13), (7,14), (7,17), (8,9), (8,11), (8,17), (9,18), (9,19... | {"n": 20, "k": 7, "edges": [[0, 5], [0, 6], [0, 9], [0, 18], [1, 5], [1, 16], [1, 17], [1, 19], [2, 7], [2, 9], [2, 10], [2, 13], [2, 15], [2, 17], [3, 9], [3, 10], [4, 9], [4, 11], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [5, 6], [6, 9], [6, 12], [6, 15], [7, 13], [7, 14], [7, 17], [8, 9], [8, 11], [8, 17], [9, 18... | null | null | null | {"independent_set": [0, 2, 3, 8, 14, 16, 19]} | 1 |
construct-mc-max-independent-set-l2-s0 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 104 edges:
(0,8), (0,9), (0,13), (0,19), (0,26), (0,27), (1,2), (1,4), (1,10), (1,11), (1,14), (1,17), (1,23), (2,3), (2,10), (2,12), (2,16), (2,23), (2,28), (2,29), (3,6), (3,8), (3,27), (3,29), (4,7), (4,12), (4,19), (4,21), (4,22), (4,23), (5,7), (5,16), (5,17), (5,19), (5... | {"n": 30, "k": 9, "edges": [[0, 8], [0, 9], [0, 13], [0, 19], [0, 26], [0, 27], [1, 2], [1, 4], [1, 10], [1, 11], [1, 14], [1, 17], [1, 23], [2, 3], [2, 10], [2, 12], [2, 16], [2, 23], [2, 28], [2, 29], [3, 6], [3, 8], [3, 27], [3, 29], [4, 7], [4, 12], [4, 19], [4, 21], [4, 22], [4, 23], [5, 7], [5, 16], [5, 17], [5, ... | null | null | null | {"independent_set": [4, 8, 10, 14, 16, 18, 20, 25, 28]} | 1 |
construct-mc-max-independent-set-l2-s1 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 136 edges:
(0,1), (0,9), (0,11), (0,13), (0,27), (1,2), (1,9), (1,17), (1,18), (1,27), (1,29), (2,6), (2,7), (2,9), (2,14), (2,20), (2,21), (2,22), (2,23), (2,28), (2,29), (3,4), (3,5), (3,10), (3,11), (3,16), (3,19), (3,21), (3,24), (3,26), (3,27), (3,28), (4,11), (4,14), (4... | {"n": 30, "k": 9, "edges": [[0, 1], [0, 9], [0, 11], [0, 13], [0, 27], [1, 2], [1, 9], [1, 17], [1, 18], [1, 27], [1, 29], [2, 6], [2, 7], [2, 9], [2, 14], [2, 20], [2, 21], [2, 22], [2, 23], [2, 28], [2, 29], [3, 4], [3, 5], [3, 10], [3, 11], [3, 16], [3, 19], [3, 21], [3, 24], [3, 26], [3, 27], [3, 28], [4, 11], [4, ... | null | null | null | {"independent_set": [0, 6, 7, 15, 17, 18, 19, 23, 29]} | 1 |
construct-mc-max-independent-set-l2-s2 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 111 edges:
(0,7), (0,10), (0,22), (0,23), (0,26), (0,27), (1,8), (1,13), (1,15), (2,5), (2,8), (2,18), (2,19), (2,23), (3,12), (3,13), (3,18), (3,29), (4,6), (4,8), (4,15), (4,16), (4,20), (4,22), (4,23), (4,24), (5,9), (5,10), (5,11), (5,13), (5,16), (5,18), (5,20), (5,24), ... | {"n": 30, "k": 9, "edges": [[0, 7], [0, 10], [0, 22], [0, 23], [0, 26], [0, 27], [1, 8], [1, 13], [1, 15], [2, 5], [2, 8], [2, 18], [2, 19], [2, 23], [3, 12], [3, 13], [3, 18], [3, 29], [4, 6], [4, 8], [4, 15], [4, 16], [4, 20], [4, 22], [4, 23], [4, 24], [5, 9], [5, 10], [5, 11], [5, 13], [5, 16], [5, 18], [5, 20], [5... | null | null | null | {"independent_set": [1, 2, 3, 4, 7, 9, 10, 25, 26]} | 1 |
construct-mc-max-independent-set-l2-s3 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 125 edges:
(0,4), (0,7), (0,9), (0,10), (0,11), (0,14), (0,15), (0,18), (0,29), (1,10), (1,13), (1,26), (1,29), (2,3), (2,7), (2,11), (2,14), (2,15), (2,17), (2,24), (2,26), (3,7), (3,9), (3,19), (3,21), (3,23), (3,26), (3,28), (4,16), (4,18), (4,20), (4,24), (4,25), (4,29), ... | {"n": 30, "k": 9, "edges": [[0, 4], [0, 7], [0, 9], [0, 10], [0, 11], [0, 14], [0, 15], [0, 18], [0, 29], [1, 10], [1, 13], [1, 26], [1, 29], [2, 3], [2, 7], [2, 11], [2, 14], [2, 15], [2, 17], [2, 24], [2, 26], [3, 7], [3, 9], [3, 19], [3, 21], [3, 23], [3, 26], [3, 28], [4, 16], [4, 18], [4, 20], [4, 24], [4, 25], [4... | null | null | null | {"independent_set": [0, 1, 2, 6, 8, 16, 21, 22, 25]} | 1 |
construct-mc-max-independent-set-l2-s4 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 123 edges:
(0,4), (0,6), (0,8), (0,15), (0,17), (0,19), (0,21), (0,22), (0,25), (0,26), (0,27), (0,29), (1,3), (1,5), (1,21), (1,25), (2,7), (2,9), (2,10), (2,13), (2,16), (2,19), (2,21), (2,27), (2,28), (3,5), (3,7), (3,10), (3,12), (3,16), (3,17), (3,19), (3,22), (3,23), (4... | {"n": 30, "k": 9, "edges": [[0, 4], [0, 6], [0, 8], [0, 15], [0, 17], [0, 19], [0, 21], [0, 22], [0, 25], [0, 26], [0, 27], [0, 29], [1, 3], [1, 5], [1, 21], [1, 25], [2, 7], [2, 9], [2, 10], [2, 13], [2, 16], [2, 19], [2, 21], [2, 27], [2, 28], [3, 5], [3, 7], [3, 10], [3, 12], [3, 16], [3, 17], [3, 19], [3, 22], [3, ... | null | null | null | {"independent_set": [1, 8, 11, 12, 15, 17, 18, 19, 29]} | 1 |
construct-mc-max-independent-set-l2-s5 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 122 edges:
(0,1), (0,9), (0,10), (0,12), (0,14), (0,15), (0,16), (0,18), (0,22), (0,23), (0,26), (0,27), (1,6), (1,7), (1,15), (1,29), (2,4), (2,6), (2,9), (2,15), (2,17), (2,28), (3,5), (3,7), (3,12), (3,15), (3,20), (3,21), (3,23), (4,15), (4,17), (4,26), (4,28), (4,29), (5... | {"n": 30, "k": 9, "edges": [[0, 1], [0, 9], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 18], [0, 22], [0, 23], [0, 26], [0, 27], [1, 6], [1, 7], [1, 15], [1, 29], [2, 4], [2, 6], [2, 9], [2, 15], [2, 17], [2, 28], [3, 5], [3, 7], [3, 12], [3, 15], [3, 20], [3, 21], [3, 23], [4, 15], [4, 17], [4, 26], [4, 28], [4, ... | null | null | null | {"independent_set": [1, 3, 4, 8, 10, 16, 22, 25, 27]} | 1 |
construct-mc-max-independent-set-l2-s6 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 114 edges:
(0,3), (0,4), (0,5), (0,12), (0,14), (0,21), (1,9), (1,15), (1,19), (1,22), (1,23), (1,29), (2,10), (2,15), (2,17), (2,19), (2,24), (2,27), (2,28), (3,7), (3,14), (3,19), (3,22), (3,23), (4,6), (4,7), (4,8), (4,16), (4,17), (4,19), (4,28), (4,29), (5,6), (5,7), (5,... | {"n": 30, "k": 9, "edges": [[0, 3], [0, 4], [0, 5], [0, 12], [0, 14], [0, 21], [1, 9], [1, 15], [1, 19], [1, 22], [1, 23], [1, 29], [2, 10], [2, 15], [2, 17], [2, 19], [2, 24], [2, 27], [2, 28], [3, 7], [3, 14], [3, 19], [3, 22], [3, 23], [4, 6], [4, 7], [4, 8], [4, 16], [4, 17], [4, 19], [4, 28], [4, 29], [5, 6], [5, ... | null | null | null | {"independent_set": [0, 6, 7, 8, 17, 20, 22, 23, 27]} | 1 |
construct-mc-max-independent-set-l2-s7 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 112 edges:
(0,1), (0,3), (0,7), (0,9), (0,13), (0,15), (0,17), (0,21), (0,23), (0,26), (1,6), (1,7), (1,8), (1,19), (1,26), (1,28), (2,6), (2,7), (2,12), (2,15), (2,17), (2,27), (2,28), (2,29), (3,7), (3,11), (3,12), (3,14), (3,15), (3,20), (3,24), (3,27), (3,28), (4,8), (4,1... | {"n": 30, "k": 9, "edges": [[0, 1], [0, 3], [0, 7], [0, 9], [0, 13], [0, 15], [0, 17], [0, 21], [0, 23], [0, 26], [1, 6], [1, 7], [1, 8], [1, 19], [1, 26], [1, 28], [2, 6], [2, 7], [2, 12], [2, 15], [2, 17], [2, 27], [2, 28], [2, 29], [3, 7], [3, 11], [3, 12], [3, 14], [3, 15], [3, 20], [3, 24], [3, 27], [3, 28], [4, 8... | null | null | null | {"independent_set": [1, 2, 10, 13, 14, 20, 23, 24, 25]} | 1 |
construct-mc-max-independent-set-l2-s8 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 120 edges:
(0,1), (0,4), (0,6), (0,8), (0,9), (0,20), (0,26), (0,27), (1,2), (1,5), (1,8), (1,11), (1,15), (1,17), (1,24), (1,29), (2,4), (2,5), (2,16), (2,20), (2,22), (2,28), (3,17), (3,19), (3,25), (4,6), (4,7), (4,8), (4,9), (4,14), (4,16), (4,17), (4,23), (4,24), (4,26),... | {"n": 30, "k": 9, "edges": [[0, 1], [0, 4], [0, 6], [0, 8], [0, 9], [0, 20], [0, 26], [0, 27], [1, 2], [1, 5], [1, 8], [1, 11], [1, 15], [1, 17], [1, 24], [1, 29], [2, 4], [2, 5], [2, 16], [2, 20], [2, 22], [2, 28], [3, 17], [3, 19], [3, 25], [4, 6], [4, 7], [4, 8], [4, 9], [4, 14], [4, 16], [4, 17], [4, 23], [4, 24], ... | null | null | null | {"independent_set": [2, 3, 8, 10, 12, 14, 18, 24, 26]} | 1 |
construct-mc-max-independent-set-l2-s9 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 2 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 30 vertices numbered 0..29 and 115 edges:
(0,4), (0,10), (0,12), (0,20), (1,7), (1,12), (1,18), (1,19), (1,22), (1,24), (1,26), (1,28), (2,3), (2,6), (2,15), (2,20), (2,22), (2,24), (2,25), (2,29), (3,5), (3,6), (3,7), (3,9), (3,22), (4,6), (4,8), (4,9), (4,16), (4,18), (4,21), (4,23), (4,24), (4,25), (4,2... | {"n": 30, "k": 9, "edges": [[0, 4], [0, 10], [0, 12], [0, 20], [1, 7], [1, 12], [1, 18], [1, 19], [1, 22], [1, 24], [1, 26], [1, 28], [2, 3], [2, 6], [2, 15], [2, 20], [2, 22], [2, 24], [2, 25], [2, 29], [3, 5], [3, 6], [3, 7], [3, 9], [3, 22], [4, 6], [4, 8], [4, 9], [4, 16], [4, 18], [4, 21], [4, 23], [4, 24], [4, 25... | null | null | null | {"independent_set": [0, 1, 3, 13, 14, 16, 21, 23, 29]} | 1 |
construct-mc-max-independent-set-l3-s0 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 55 vertices numbered 0..54 and 441 edges:
(0,3), (0,7), (0,8), (0,14), (0,16), (0,17), (0,18), (0,20), (0,21), (0,22), (0,23), (0,28), (0,32), (0,33), (0,34), (0,42), (0,48), (0,50), (0,54), (1,4), (1,8), (1,9), (1,11), (1,14), (1,18), (1,20), (1,34), (1,46), (1,50), (1,52), (2,5), (2,7), (2,12), (2,14), (... | {"n": 55, "k": 13, "edges": [[0, 3], [0, 7], [0, 8], [0, 14], [0, 16], [0, 17], [0, 18], [0, 20], [0, 21], [0, 22], [0, 23], [0, 28], [0, 32], [0, 33], [0, 34], [0, 42], [0, 48], [0, 50], [0, 54], [1, 4], [1, 8], [1, 9], [1, 11], [1, 14], [1, 18], [1, 20], [1, 34], [1, 46], [1, 50], [1, 52], [2, 5], [2, 7], [2, 12], [2... | null | null | null | {"independent_set": [6, 7, 14, 18, 19, 21, 24, 26, 34, 37, 43, 53, 54]} | 1 |
construct-mc-max-independent-set-l3-s1 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 270 edges:
(0,11), (0,16), (0,17), (0,19), (0,22), (0,25), (0,26), (0,27), (0,31), (0,32), (0,34), (0,36), (0,37), (0,40), (0,44), (1,2), (1,4), (1,10), (1,11), (1,14), (1,18), (1,19), (1,20), (1,21), (1,28), (1,30), (1,37), (1,39), (1,40), (1,42), (2,3), (2,7), (2,13), (2,14... | {"n": 45, "k": 11, "edges": [[0, 11], [0, 16], [0, 17], [0, 19], [0, 22], [0, 25], [0, 26], [0, 27], [0, 31], [0, 32], [0, 34], [0, 36], [0, 37], [0, 40], [0, 44], [1, 2], [1, 4], [1, 10], [1, 11], [1, 14], [1, 18], [1, 19], [1, 20], [1, 21], [1, 28], [1, 30], [1, 37], [1, 39], [1, 40], [1, 42], [2, 3], [2, 7], [2, 13]... | null | null | null | {"independent_set": [2, 4, 5, 10, 11, 17, 20, 34, 36, 40, 44]} | 1 |
construct-mc-max-independent-set-l3-s2 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 285 edges:
(0,8), (0,18), (0,19), (0,23), (0,24), (0,25), (0,30), (0,31), (0,34), (0,36), (0,38), (0,41), (0,42), (1,5), (1,13), (1,16), (1,18), (1,21), (1,26), (1,32), (1,34), (1,44), (2,4), (2,5), (2,7), (2,8), (2,13), (2,15), (2,16), (2,20), (2,21), (2,24), (2,26), (2,33),... | {"n": 45, "k": 11, "edges": [[0, 8], [0, 18], [0, 19], [0, 23], [0, 24], [0, 25], [0, 30], [0, 31], [0, 34], [0, 36], [0, 38], [0, 41], [0, 42], [1, 5], [1, 13], [1, 16], [1, 18], [1, 21], [1, 26], [1, 32], [1, 34], [1, 44], [2, 4], [2, 5], [2, 7], [2, 8], [2, 13], [2, 15], [2, 16], [2, 20], [2, 21], [2, 24], [2, 26], ... | null | null | null | {"independent_set": [1, 6, 17, 23, 27, 28, 30, 35, 39, 40, 42]} | 1 |
construct-mc-max-independent-set-l3-s3 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 279 edges:
(0,2), (0,6), (0,16), (0,21), (0,22), (0,23), (0,29), (0,30), (0,32), (0,33), (0,35), (0,36), (0,39), (1,12), (1,16), (1,24), (1,30), (1,37), (1,42), (1,44), (2,3), (2,7), (2,8), (2,12), (2,16), (2,21), (2,23), (2,29), (2,31), (2,32), (2,33), (2,37), (2,39), (2,40)... | {"n": 45, "k": 11, "edges": [[0, 2], [0, 6], [0, 16], [0, 21], [0, 22], [0, 23], [0, 29], [0, 30], [0, 32], [0, 33], [0, 35], [0, 36], [0, 39], [1, 12], [1, 16], [1, 24], [1, 30], [1, 37], [1, 42], [1, 44], [2, 3], [2, 7], [2, 8], [2, 12], [2, 16], [2, 21], [2, 23], [2, 29], [2, 31], [2, 32], [2, 33], [2, 37], [2, 39],... | null | null | null | {"independent_set": [1, 6, 7, 9, 10, 13, 18, 26, 33, 41, 43]} | 1 |
construct-mc-max-independent-set-l3-s4 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 275 edges:
(0,8), (0,11), (0,22), (0,24), (0,30), (0,33), (0,36), (0,38), (0,40), (0,41), (0,42), (0,43), (0,44), (1,3), (1,9), (1,15), (1,18), (1,29), (1,33), (1,34), (1,35), (1,36), (1,44), (2,6), (2,8), (2,9), (2,13), (2,19), (2,21), (2,30), (2,31), (2,32), (2,38), (2,40),... | {"n": 45, "k": 11, "edges": [[0, 8], [0, 11], [0, 22], [0, 24], [0, 30], [0, 33], [0, 36], [0, 38], [0, 40], [0, 41], [0, 42], [0, 43], [0, 44], [1, 3], [1, 9], [1, 15], [1, 18], [1, 29], [1, 33], [1, 34], [1, 35], [1, 36], [1, 44], [2, 6], [2, 8], [2, 9], [2, 13], [2, 19], [2, 21], [2, 30], [2, 31], [2, 32], [2, 38], ... | null | null | null | {"independent_set": [15, 21, 23, 31, 32, 37, 39, 40, 42, 43, 44]} | 1 |
construct-mc-max-independent-set-l3-s5 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 264 edges:
(0,1), (0,2), (0,5), (0,7), (0,10), (0,26), (0,28), (0,33), (0,36), (0,37), (0,41), (0,42), (1,3), (1,14), (1,16), (1,19), (1,21), (1,24), (1,27), (1,29), (1,32), (1,33), (1,36), (1,38), (1,42), (2,4), (2,6), (2,14), (2,23), (2,25), (2,27), (2,32), (2,33), (2,36), ... | {"n": 45, "k": 11, "edges": [[0, 1], [0, 2], [0, 5], [0, 7], [0, 10], [0, 26], [0, 28], [0, 33], [0, 36], [0, 37], [0, 41], [0, 42], [1, 3], [1, 14], [1, 16], [1, 19], [1, 21], [1, 24], [1, 27], [1, 29], [1, 32], [1, 33], [1, 36], [1, 38], [1, 42], [2, 4], [2, 6], [2, 14], [2, 23], [2, 25], [2, 27], [2, 32], [2, 33], [... | null | null | null | {"independent_set": [1, 2, 8, 9, 20, 26, 28, 34, 35, 40, 44]} | 1 |
construct-mc-max-independent-set-l3-s6 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 288 edges:
(0,2), (0,6), (0,9), (0,11), (0,12), (0,14), (0,15), (0,17), (0,18), (0,22), (0,25), (0,33), (0,36), (0,37), (0,39), (0,40), (1,3), (1,10), (1,17), (1,20), (1,22), (1,23), (2,5), (2,6), (2,10), (2,11), (2,13), (2,14), (2,15), (2,16), (2,17), (2,19), (2,21), (2,22),... | {"n": 45, "k": 11, "edges": [[0, 2], [0, 6], [0, 9], [0, 11], [0, 12], [0, 14], [0, 15], [0, 17], [0, 18], [0, 22], [0, 25], [0, 33], [0, 36], [0, 37], [0, 39], [0, 40], [1, 3], [1, 10], [1, 17], [1, 20], [1, 22], [1, 23], [2, 5], [2, 6], [2, 10], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 19], [2, 21], ... | null | null | null | {"independent_set": [9, 11, 13, 18, 19, 24, 31, 32, 39, 41, 44]} | 1 |
construct-mc-max-independent-set-l3-s7 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 266 edges:
(0,3), (0,4), (0,5), (0,9), (0,10), (0,14), (0,15), (0,17), (0,18), (0,23), (0,27), (0,28), (0,32), (0,39), (1,5), (1,6), (1,8), (1,9), (1,14), (1,15), (1,19), (1,20), (1,27), (1,35), (1,39), (1,40), (1,41), (2,4), (2,10), (2,11), (2,17), (2,18), (2,20), (2,21), (2... | {"n": 45, "k": 11, "edges": [[0, 3], [0, 4], [0, 5], [0, 9], [0, 10], [0, 14], [0, 15], [0, 17], [0, 18], [0, 23], [0, 27], [0, 28], [0, 32], [0, 39], [1, 5], [1, 6], [1, 8], [1, 9], [1, 14], [1, 15], [1, 19], [1, 20], [1, 27], [1, 35], [1, 39], [1, 40], [1, 41], [2, 4], [2, 10], [2, 11], [2, 17], [2, 18], [2, 20], [2,... | null | null | null | {"independent_set": [4, 5, 6, 8, 9, 16, 26, 28, 32, 34, 39]} | 1 |
construct-mc-max-independent-set-l3-s8 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 276 edges:
(0,9), (0,12), (0,13), (0,15), (0,17), (0,19), (0,20), (0,23), (0,27), (0,30), (0,32), (0,40), (0,43), (1,7), (1,10), (1,13), (1,18), (1,22), (1,23), (1,25), (1,27), (1,28), (1,30), (1,32), (1,33), (1,36), (2,6), (2,8), (2,10), (2,12), (2,15), (2,33), (2,34), (2,38... | {"n": 45, "k": 11, "edges": [[0, 9], [0, 12], [0, 13], [0, 15], [0, 17], [0, 19], [0, 20], [0, 23], [0, 27], [0, 30], [0, 32], [0, 40], [0, 43], [1, 7], [1, 10], [1, 13], [1, 18], [1, 22], [1, 23], [1, 25], [1, 27], [1, 28], [1, 30], [1, 32], [1, 33], [1, 36], [2, 6], [2, 8], [2, 10], [2, 12], [2, 15], [2, 33], [2, 34]... | null | null | null | {"independent_set": [2, 9, 13, 16, 22, 23, 24, 29, 32, 37, 42]} | 1 |
construct-mc-max-independent-set-l3-s9 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 3 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 271 edges:
(0,5), (0,6), (0,7), (0,13), (0,14), (0,27), (0,32), (0,35), (0,36), (0,39), (0,40), (0,43), (1,5), (1,11), (1,13), (1,14), (1,18), (1,21), (1,34), (1,35), (1,37), (1,43), (2,7), (2,14), (2,15), (2,16), (2,17), (2,19), (2,21), (2,23), (2,38), (2,40), (2,42), (3,4),... | {"n": 45, "k": 11, "edges": [[0, 5], [0, 6], [0, 7], [0, 13], [0, 14], [0, 27], [0, 32], [0, 35], [0, 36], [0, 39], [0, 40], [0, 43], [1, 5], [1, 11], [1, 13], [1, 14], [1, 18], [1, 21], [1, 34], [1, 35], [1, 37], [1, 43], [2, 7], [2, 14], [2, 15], [2, 16], [2, 17], [2, 19], [2, 21], [2, 23], [2, 38], [2, 40], [2, 42],... | null | null | null | {"independent_set": [2, 5, 6, 9, 12, 22, 26, 33, 34, 35, 37]} | 1 |
construct-mc-max-independent-set-l4-s0 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 499 edges:
(0,3), (0,4), (0,6), (0,8), (0,10), (0,18), (0,19), (0,20), (0,21), (0,26), (0,29), (0,34), (0,36), (0,41), (0,45), (0,49), (0,53), (0,56), (0,57), (0,58), (0,59), (1,2), (1,5), (1,7), (1,9), (1,15), (1,16), (1,17), (1,21), (1,28), (1,31), (1,35), (1,39), (1,48), (... | {"n": 60, "k": 14, "edges": [[0, 3], [0, 4], [0, 6], [0, 8], [0, 10], [0, 18], [0, 19], [0, 20], [0, 21], [0, 26], [0, 29], [0, 34], [0, 36], [0, 41], [0, 45], [0, 49], [0, 53], [0, 56], [0, 57], [0, 58], [0, 59], [1, 2], [1, 5], [1, 7], [1, 9], [1, 15], [1, 16], [1, 17], [1, 21], [1, 28], [1, 31], [1, 35], [1, 39], [1... | null | null | null | {"independent_set": [1, 3, 8, 13, 19, 22, 23, 25, 33, 37, 38, 44, 54, 57]} | 1 |
construct-mc-max-independent-set-l4-s1 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 502 edges:
(0,2), (0,4), (0,6), (0,8), (0,19), (0,28), (0,33), (0,36), (0,42), (0,44), (0,47), (0,52), (0,57), (1,3), (1,4), (1,5), (1,7), (1,8), (1,9), (1,12), (1,18), (1,19), (1,24), (1,28), (1,31), (1,32), (1,33), (1,41), (1,44), (1,45), (1,46), (1,54), (2,8), (2,9), (2,13... | {"n": 60, "k": 14, "edges": [[0, 2], [0, 4], [0, 6], [0, 8], [0, 19], [0, 28], [0, 33], [0, 36], [0, 42], [0, 44], [0, 47], [0, 52], [0, 57], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 12], [1, 18], [1, 19], [1, 24], [1, 28], [1, 31], [1, 32], [1, 33], [1, 41], [1, 44], [1, 45], [1, 46], [1, 54], [2, 8], [2, 9... | null | null | null | {"independent_set": [0, 7, 14, 20, 23, 25, 30, 37, 45, 50, 51, 53, 56, 58]} | 1 |
construct-mc-max-independent-set-l4-s2 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 484 edges:
(0,1), (0,3), (0,4), (0,5), (0,7), (0,10), (0,13), (0,14), (0,16), (0,19), (0,21), (0,24), (0,26), (0,32), (0,40), (0,42), (0,43), (0,45), (0,59), (1,12), (1,13), (1,15), (1,16), (1,17), (1,20), (1,22), (1,28), (1,31), (1,46), (1,52), (1,54), (1,57), (2,3), (2,4), ... | {"n": 60, "k": 14, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 13], [0, 14], [0, 16], [0, 19], [0, 21], [0, 24], [0, 26], [0, 32], [0, 40], [0, 42], [0, 43], [0, 45], [0, 59], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 20], [1, 22], [1, 28], [1, 31], [1, 46], [1, 52], [1, 54], [1, 57], [2, 3], ... | null | null | null | {"independent_set": [2, 10, 13, 15, 16, 18, 22, 29, 32, 41, 42, 45, 54, 59]} | 1 |
construct-mc-max-independent-set-l4-s3 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 480 edges:
(0,2), (0,4), (0,6), (0,8), (0,9), (0,11), (0,12), (0,17), (0,21), (0,22), (0,23), (0,25), (0,28), (0,36), (0,37), (0,39), (0,41), (0,44), (0,45), (0,49), (0,51), (0,52), (1,10), (1,11), (1,24), (1,27), (1,34), (1,35), (1,36), (1,44), (1,47), (1,48), (1,59), (2,5),... | {"n": 60, "k": 14, "edges": [[0, 2], [0, 4], [0, 6], [0, 8], [0, 9], [0, 11], [0, 12], [0, 17], [0, 21], [0, 22], [0, 23], [0, 25], [0, 28], [0, 36], [0, 37], [0, 39], [0, 41], [0, 44], [0, 45], [0, 49], [0, 51], [0, 52], [1, 10], [1, 11], [1, 24], [1, 27], [1, 34], [1, 35], [1, 36], [1, 44], [1, 47], [1, 48], [1, 59],... | null | null | null | {"independent_set": [2, 8, 11, 12, 13, 14, 15, 16, 20, 22, 31, 37, 40, 42]} | 1 |
construct-mc-max-independent-set-l4-s4 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 517 edges:
(0,11), (0,13), (0,15), (0,17), (0,26), (0,33), (0,35), (0,37), (0,38), (0,52), (0,54), (0,55), (0,57), (1,3), (1,6), (1,12), (1,20), (1,22), (1,27), (1,28), (1,34), (1,36), (1,39), (1,43), (1,45), (1,47), (1,48), (1,49), (1,55), (1,57), (2,3), (2,14), (2,15), (2,1... | {"n": 60, "k": 14, "edges": [[0, 11], [0, 13], [0, 15], [0, 17], [0, 26], [0, 33], [0, 35], [0, 37], [0, 38], [0, 52], [0, 54], [0, 55], [0, 57], [1, 3], [1, 6], [1, 12], [1, 20], [1, 22], [1, 27], [1, 28], [1, 34], [1, 36], [1, 39], [1, 43], [1, 45], [1, 47], [1, 48], [1, 49], [1, 55], [1, 57], [2, 3], [2, 14], [2, 15... | null | null | null | {"independent_set": [0, 2, 6, 8, 9, 10, 12, 21, 25, 36, 41, 47, 50, 51]} | 1 |
construct-mc-max-independent-set-l4-s5 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 494 edges:
(0,1), (0,5), (0,10), (0,16), (0,18), (0,21), (0,22), (0,25), (0,31), (0,33), (0,34), (0,40), (0,54), (0,57), (0,59), (1,7), (1,10), (1,11), (1,15), (1,16), (1,17), (1,18), (1,19), (1,20), (1,21), (1,27), (1,28), (1,31), (1,33), (1,39), (1,41), (1,43), (1,47), (1,4... | {"n": 60, "k": 14, "edges": [[0, 1], [0, 5], [0, 10], [0, 16], [0, 18], [0, 21], [0, 22], [0, 25], [0, 31], [0, 33], [0, 34], [0, 40], [0, 54], [0, 57], [0, 59], [1, 7], [1, 10], [1, 11], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 27], [1, 28], [1, 31], [1, 33], [1, 39], [1, 41], [1, 43], [1, 47... | null | null | null | {"independent_set": [4, 8, 16, 17, 19, 21, 36, 37, 49, 50, 51, 55, 58, 59]} | 1 |
construct-mc-max-independent-set-l4-s6 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 496 edges:
(0,7), (0,8), (0,13), (0,14), (0,15), (0,21), (0,24), (0,25), (0,32), (0,41), (0,42), (0,49), (0,58), (1,4), (1,9), (1,12), (1,14), (1,18), (1,24), (1,25), (1,26), (1,27), (1,28), (1,29), (1,30), (1,35), (1,41), (1,44), (1,57), (1,58), (1,59), (2,16), (2,20), (2,26... | {"n": 60, "k": 14, "edges": [[0, 7], [0, 8], [0, 13], [0, 14], [0, 15], [0, 21], [0, 24], [0, 25], [0, 32], [0, 41], [0, 42], [0, 49], [0, 58], [1, 4], [1, 9], [1, 12], [1, 14], [1, 18], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 35], [1, 41], [1, 44], [1, 57], [1, 58], [1, 59], [2, 16], [2, 20]... | null | null | null | {"independent_set": [8, 26, 29, 31, 32, 33, 34, 38, 39, 41, 44, 49, 56, 57]} | 1 |
construct-mc-max-independent-set-l4-s7 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 502 edges:
(0,1), (0,4), (0,6), (0,8), (0,17), (0,20), (0,27), (0,35), (0,40), (0,43), (0,45), (0,46), (0,47), (0,48), (0,50), (0,52), (0,57), (1,3), (1,4), (1,10), (1,11), (1,13), (1,14), (1,15), (1,16), (1,21), (1,23), (1,27), (1,28), (1,29), (1,38), (1,47), (1,48), (1,53),... | {"n": 60, "k": 14, "edges": [[0, 1], [0, 4], [0, 6], [0, 8], [0, 17], [0, 20], [0, 27], [0, 35], [0, 40], [0, 43], [0, 45], [0, 46], [0, 47], [0, 48], [0, 50], [0, 52], [0, 57], [1, 3], [1, 4], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [1, 21], [1, 23], [1, 27], [1, 28], [1, 29], [1, 38], [1, 47], [1, 48], ... | null | null | null | {"independent_set": [6, 8, 10, 16, 22, 31, 33, 38, 44, 48, 53, 55, 57, 58]} | 1 |
construct-mc-max-independent-set-l4-s8 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 498 edges:
(0,2), (0,3), (0,8), (0,12), (0,18), (0,24), (0,33), (0,34), (0,36), (0,39), (0,46), (0,49), (0,50), (0,53), (0,55), (1,4), (1,8), (1,15), (1,21), (1,40), (1,53), (1,55), (2,4), (2,5), (2,8), (2,9), (2,10), (2,11), (2,14), (2,20), (2,22), (2,24), (2,36), (2,41), (2... | {"n": 60, "k": 14, "edges": [[0, 2], [0, 3], [0, 8], [0, 12], [0, 18], [0, 24], [0, 33], [0, 34], [0, 36], [0, 39], [0, 46], [0, 49], [0, 50], [0, 53], [0, 55], [1, 4], [1, 8], [1, 15], [1, 21], [1, 40], [1, 53], [1, 55], [2, 4], [2, 5], [2, 8], [2, 9], [2, 10], [2, 11], [2, 14], [2, 20], [2, 22], [2, 24], [2, 36], [2,... | null | null | null | {"independent_set": [0, 1, 10, 20, 22, 23, 29, 30, 42, 44, 48, 52, 54, 59]} | 1 |
construct-mc-max-independent-set-l4-s9 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 4 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 528 edges:
(0,7), (0,11), (0,13), (0,17), (0,34), (0,35), (0,38), (0,41), (0,42), (0,47), (0,48), (0,53), (0,56), (0,57), (1,4), (1,9), (1,10), (1,14), (1,19), (1,26), (1,28), (1,29), (1,34), (1,43), (1,45), (1,46), (1,48), (1,50), (1,54), (2,4), (2,6), (2,9), (2,11), (2,13),... | {"n": 60, "k": 14, "edges": [[0, 7], [0, 11], [0, 13], [0, 17], [0, 34], [0, 35], [0, 38], [0, 41], [0, 42], [0, 47], [0, 48], [0, 53], [0, 56], [0, 57], [1, 4], [1, 9], [1, 10], [1, 14], [1, 19], [1, 26], [1, 28], [1, 29], [1, 34], [1, 43], [1, 45], [1, 46], [1, 48], [1, 50], [1, 54], [2, 4], [2, 6], [2, 9], [2, 11], ... | null | null | null | {"independent_set": [7, 14, 16, 18, 20, 21, 28, 29, 30, 31, 39, 49, 55, 57]} | 1 |
construct-mc-max-independent-set-l5-s0 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1195 edges:
(0,13), (0,18), (0,23), (0,24), (0,35), (0,44), (0,46), (0,52), (0,53), (0,58), (0,60), (0,61), (0,63), (0,70), (0,81), (0,88), (1,3), (1,10), (1,15), (1,19), (1,20), (1,21), (1,22), (1,23), (1,25), (1,27), (1,28), (1,29), (1,32), (1,35), (1,43), (1,47), (1,48), (... | {"n": 90, "k": 16, "edges": [[0, 13], [0, 18], [0, 23], [0, 24], [0, 35], [0, 44], [0, 46], [0, 52], [0, 53], [0, 58], [0, 60], [0, 61], [0, 63], [0, 70], [0, 81], [0, 88], [1, 3], [1, 10], [1, 15], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 25], [1, 27], [1, 28], [1, 29], [1, 32], [1, 35], [1, 43], [1, 47], [1, ... | null | null | null | {"independent_set": [0, 2, 3, 4, 5, 6, 15, 19, 38, 45, 55, 67, 80, 83, 86, 87]} | 1 |
construct-mc-max-independent-set-l5-s1 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1203 edges:
(0,4), (0,5), (0,6), (0,10), (0,15), (0,17), (0,23), (0,24), (0,28), (0,31), (0,32), (0,42), (0,44), (0,51), (0,54), (0,56), (0,57), (0,59), (0,60), (0,61), (0,62), (0,63), (0,64), (0,67), (0,68), (0,71), (0,74), (0,77), (0,81), (0,84), (0,85), (1,2), (1,3), (1,6)... | {"n": 90, "k": 16, "edges": [[0, 4], [0, 5], [0, 6], [0, 10], [0, 15], [0, 17], [0, 23], [0, 24], [0, 28], [0, 31], [0, 32], [0, 42], [0, 44], [0, 51], [0, 54], [0, 56], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 63], [0, 64], [0, 67], [0, 68], [0, 71], [0, 74], [0, 77], [0, 81], [0, 84], [0, 85], [1, 2], [1, 3],... | null | null | null | {"independent_set": [16, 24, 29, 31, 32, 41, 44, 45, 49, 55, 71, 78, 79, 80, 87, 89]} | 1 |
construct-mc-max-independent-set-l5-s2 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1180 edges:
(0,3), (0,5), (0,6), (0,8), (0,9), (0,10), (0,12), (0,13), (0,15), (0,26), (0,27), (0,41), (0,47), (0,49), (0,52), (0,53), (0,54), (0,57), (0,58), (0,61), (0,64), (0,66), (0,73), (0,79), (0,80), (0,82), (1,7), (1,9), (1,15), (1,16), (1,17), (1,27), (1,31), (1,32),... | {"n": 90, "k": 16, "edges": [[0, 3], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 12], [0, 13], [0, 15], [0, 26], [0, 27], [0, 41], [0, 47], [0, 49], [0, 52], [0, 53], [0, 54], [0, 57], [0, 58], [0, 61], [0, 64], [0, 66], [0, 73], [0, 79], [0, 80], [0, 82], [1, 7], [1, 9], [1, 15], [1, 16], [1, 17], [1, 27], [1, 31], [... | null | null | null | {"independent_set": [1, 3, 11, 12, 22, 25, 26, 34, 39, 44, 65, 76, 80, 83, 85, 87]} | 1 |
construct-mc-max-independent-set-l5-s3 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1129 edges:
(0,1), (0,2), (0,3), (0,9), (0,11), (0,17), (0,19), (0,22), (0,29), (0,31), (0,32), (0,37), (0,41), (0,46), (0,56), (0,62), (0,63), (0,64), (0,65), (0,69), (0,73), (0,76), (0,77), (0,78), (0,79), (0,87), (1,10), (1,14), (1,18), (1,19), (1,21), (1,22), (1,30), (1,3... | {"n": 90, "k": 16, "edges": [[0, 1], [0, 2], [0, 3], [0, 9], [0, 11], [0, 17], [0, 19], [0, 22], [0, 29], [0, 31], [0, 32], [0, 37], [0, 41], [0, 46], [0, 56], [0, 62], [0, 63], [0, 64], [0, 65], [0, 69], [0, 73], [0, 76], [0, 77], [0, 78], [0, 79], [0, 87], [1, 10], [1, 14], [1, 18], [1, 19], [1, 21], [1, 22], [1, 30]... | null | null | null | {"independent_set": [0, 20, 26, 27, 38, 45, 52, 53, 61, 70, 72, 74, 80, 83, 85, 86]} | 1 |
construct-mc-max-independent-set-l5-s4 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1188 edges:
(0,2), (0,4), (0,7), (0,8), (0,12), (0,14), (0,17), (0,18), (0,21), (0,22), (0,23), (0,25), (0,26), (0,28), (0,31), (0,32), (0,33), (0,38), (0,40), (0,41), (0,47), (0,49), (0,52), (0,53), (0,54), (0,55), (0,59), (0,71), (0,76), (0,77), (0,81), (0,89), (1,4), (1,11... | {"n": 90, "k": 16, "edges": [[0, 2], [0, 4], [0, 7], [0, 8], [0, 12], [0, 14], [0, 17], [0, 18], [0, 21], [0, 22], [0, 23], [0, 25], [0, 26], [0, 28], [0, 31], [0, 32], [0, 33], [0, 38], [0, 40], [0, 41], [0, 47], [0, 49], [0, 52], [0, 53], [0, 54], [0, 55], [0, 59], [0, 71], [0, 76], [0, 77], [0, 81], [0, 89], [1, 4],... | null | null | null | {"independent_set": [2, 4, 6, 7, 14, 20, 27, 30, 44, 50, 57, 59, 64, 65, 66, 84]} | 1 |
construct-mc-max-independent-set-l5-s5 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1111 edges:
(0,1), (0,2), (0,6), (0,7), (0,8), (0,11), (0,18), (0,20), (0,21), (0,33), (0,34), (0,38), (0,46), (0,47), (0,49), (0,60), (0,63), (0,66), (0,72), (0,77), (0,81), (0,82), (0,84), (1,5), (1,6), (1,10), (1,11), (1,13), (1,14), (1,20), (1,23), (1,24), (1,25), (1,40),... | {"n": 90, "k": 16, "edges": [[0, 1], [0, 2], [0, 6], [0, 7], [0, 8], [0, 11], [0, 18], [0, 20], [0, 21], [0, 33], [0, 34], [0, 38], [0, 46], [0, 47], [0, 49], [0, 60], [0, 63], [0, 66], [0, 72], [0, 77], [0, 81], [0, 82], [0, 84], [1, 5], [1, 6], [1, 10], [1, 11], [1, 13], [1, 14], [1, 20], [1, 23], [1, 24], [1, 25], [... | null | null | null | {"independent_set": [21, 24, 33, 34, 35, 45, 46, 53, 54, 62, 66, 69, 75, 77, 80, 89]} | 1 |
construct-mc-max-independent-set-l5-s6 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1115 edges:
(0,1), (0,5), (0,6), (0,9), (0,11), (0,14), (0,15), (0,22), (0,24), (0,25), (0,26), (0,28), (0,36), (0,39), (0,46), (0,51), (0,52), (0,57), (0,62), (0,68), (0,70), (0,71), (0,74), (0,79), (0,81), (0,82), (0,83), (0,86), (1,4), (1,7), (1,8), (1,12), (1,21), (1,26),... | {"n": 90, "k": 16, "edges": [[0, 1], [0, 5], [0, 6], [0, 9], [0, 11], [0, 14], [0, 15], [0, 22], [0, 24], [0, 25], [0, 26], [0, 28], [0, 36], [0, 39], [0, 46], [0, 51], [0, 52], [0, 57], [0, 62], [0, 68], [0, 70], [0, 71], [0, 74], [0, 79], [0, 81], [0, 82], [0, 83], [0, 86], [1, 4], [1, 7], [1, 8], [1, 12], [1, 21], [... | null | null | null | {"independent_set": [2, 9, 11, 13, 25, 35, 36, 37, 54, 61, 65, 68, 70, 76, 80, 88]} | 1 |
construct-mc-max-independent-set-l5-s7 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1142 edges:
(0,6), (0,12), (0,14), (0,15), (0,17), (0,19), (0,21), (0,23), (0,26), (0,27), (0,32), (0,35), (0,38), (0,45), (0,48), (0,58), (0,60), (0,64), (0,66), (0,68), (0,70), (0,77), (0,78), (0,84), (0,86), (0,88), (0,89), (1,4), (1,7), (1,8), (1,13), (1,20), (1,23), (1,2... | {"n": 90, "k": 16, "edges": [[0, 6], [0, 12], [0, 14], [0, 15], [0, 17], [0, 19], [0, 21], [0, 23], [0, 26], [0, 27], [0, 32], [0, 35], [0, 38], [0, 45], [0, 48], [0, 58], [0, 60], [0, 64], [0, 66], [0, 68], [0, 70], [0, 77], [0, 78], [0, 84], [0, 86], [0, 88], [0, 89], [1, 4], [1, 7], [1, 8], [1, 13], [1, 20], [1, 23]... | null | null | null | {"independent_set": [6, 18, 28, 32, 34, 36, 55, 59, 65, 68, 72, 77, 81, 82, 87, 88]} | 1 |
construct-mc-max-independent-set-l5-s8 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1172 edges:
(0,7), (0,9), (0,14), (0,17), (0,18), (0,28), (0,33), (0,35), (0,41), (0,42), (0,45), (0,55), (0,61), (0,63), (0,65), (0,80), (0,85), (0,86), (0,87), (1,4), (1,5), (1,9), (1,10), (1,16), (1,21), (1,28), (1,29), (1,33), (1,34), (1,37), (1,41), (1,42), (1,43), (1,48... | {"n": 90, "k": 16, "edges": [[0, 7], [0, 9], [0, 14], [0, 17], [0, 18], [0, 28], [0, 33], [0, 35], [0, 41], [0, 42], [0, 45], [0, 55], [0, 61], [0, 63], [0, 65], [0, 80], [0, 85], [0, 86], [0, 87], [1, 4], [1, 5], [1, 9], [1, 10], [1, 16], [1, 21], [1, 28], [1, 29], [1, 33], [1, 34], [1, 37], [1, 41], [1, 42], [1, 43],... | null | null | null | {"independent_set": [3, 6, 17, 27, 35, 36, 37, 38, 49, 52, 54, 55, 59, 75, 82, 84]} | 1 |
construct-mc-max-independent-set-l5-s9 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 5 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 90 vertices numbered 0..89 and 1190 edges:
(0,6), (0,9), (0,19), (0,22), (0,26), (0,27), (0,29), (0,30), (0,33), (0,41), (0,45), (0,53), (0,55), (0,57), (0,65), (0,67), (0,70), (0,77), (0,80), (0,83), (0,84), (0,89), (1,7), (1,12), (1,15), (1,17), (1,18), (1,19), (1,23), (1,25), (1,27), (1,32), (1,33), (1,... | {"n": 90, "k": 16, "edges": [[0, 6], [0, 9], [0, 19], [0, 22], [0, 26], [0, 27], [0, 29], [0, 30], [0, 33], [0, 41], [0, 45], [0, 53], [0, 55], [0, 57], [0, 65], [0, 67], [0, 70], [0, 77], [0, 80], [0, 83], [0, 84], [0, 89], [1, 7], [1, 12], [1, 15], [1, 17], [1, 18], [1, 19], [1, 23], [1, 25], [1, 27], [1, 32], [1, 33... | null | null | null | {"independent_set": [16, 19, 26, 30, 40, 44, 46, 52, 56, 57, 71, 81, 82, 85, 87, 88]} | 1 |
construct-mc-max-independent-set-l6-s0 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2877 edges:
(0,5), (0,6), (0,7), (0,17), (0,20), (0,23), (0,24), (0,26), (0,28), (0,29), (0,32), (0,34), (0,42), (0,44), (0,46), (0,49), (0,51), (0,56), (0,62), (0,64), (0,71), (0,73), (0,74), (0,77), (0,80), (0,81), (0,84), (0,85), (0,92), (0,96), (0,99), (0,103), (0,106),... | {"n": 140, "k": 18, "edges": [[0, 5], [0, 6], [0, 7], [0, 17], [0, 20], [0, 23], [0, 24], [0, 26], [0, 28], [0, 29], [0, 32], [0, 34], [0, 42], [0, 44], [0, 46], [0, 49], [0, 51], [0, 56], [0, 62], [0, 64], [0, 71], [0, 73], [0, 74], [0, 77], [0, 80], [0, 81], [0, 84], [0, 85], [0, 92], [0, 96], [0, 99], [0, 103], [0, ... | null | null | null | {"independent_set": [2, 8, 14, 15, 35, 39, 52, 57, 60, 65, 76, 83, 84, 95, 105, 117, 121, 125]} | 1 |
construct-mc-max-independent-set-l6-s1 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2915 edges:
(0,12), (0,13), (0,18), (0,19), (0,20), (0,25), (0,26), (0,27), (0,31), (0,34), (0,35), (0,37), (0,38), (0,49), (0,53), (0,54), (0,56), (0,59), (0,60), (0,63), (0,68), (0,71), (0,73), (0,75), (0,78), (0,80), (0,81), (0,84), (0,85), (0,87), (0,88), (0,93), (0,95)... | {"n": 140, "k": 18, "edges": [[0, 12], [0, 13], [0, 18], [0, 19], [0, 20], [0, 25], [0, 26], [0, 27], [0, 31], [0, 34], [0, 35], [0, 37], [0, 38], [0, 49], [0, 53], [0, 54], [0, 56], [0, 59], [0, 60], [0, 63], [0, 68], [0, 71], [0, 73], [0, 75], [0, 78], [0, 80], [0, 81], [0, 84], [0, 85], [0, 87], [0, 88], [0, 93], [0... | null | null | null | {"independent_set": [1, 2, 4, 8, 27, 41, 60, 61, 72, 73, 93, 109, 110, 114, 119, 126, 131, 139]} | 1 |
construct-mc-max-independent-set-l6-s2 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2934 edges:
(0,6), (0,14), (0,16), (0,19), (0,21), (0,23), (0,24), (0,27), (0,29), (0,31), (0,32), (0,33), (0,36), (0,37), (0,43), (0,45), (0,47), (0,48), (0,50), (0,56), (0,62), (0,64), (0,65), (0,74), (0,77), (0,83), (0,88), (0,91), (0,93), (0,100), (0,101), (0,102), (0,1... | {"n": 140, "k": 18, "edges": [[0, 6], [0, 14], [0, 16], [0, 19], [0, 21], [0, 23], [0, 24], [0, 27], [0, 29], [0, 31], [0, 32], [0, 33], [0, 36], [0, 37], [0, 43], [0, 45], [0, 47], [0, 48], [0, 50], [0, 56], [0, 62], [0, 64], [0, 65], [0, 74], [0, 77], [0, 83], [0, 88], [0, 91], [0, 93], [0, 100], [0, 101], [0, 102], ... | null | null | null | {"independent_set": [3, 6, 14, 15, 16, 23, 36, 59, 63, 64, 67, 76, 79, 86, 113, 126, 132, 137]} | 1 |
construct-mc-max-independent-set-l6-s3 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2793 edges:
(0,2), (0,6), (0,7), (0,11), (0,12), (0,15), (0,17), (0,20), (0,21), (0,24), (0,27), (0,28), (0,29), (0,39), (0,42), (0,43), (0,49), (0,56), (0,58), (0,60), (0,61), (0,66), (0,70), (0,71), (0,74), (0,80), (0,91), (0,94), (0,95), (0,96), (0,97), (0,104), (0,110),... | {"n": 140, "k": 18, "edges": [[0, 2], [0, 6], [0, 7], [0, 11], [0, 12], [0, 15], [0, 17], [0, 20], [0, 21], [0, 24], [0, 27], [0, 28], [0, 29], [0, 39], [0, 42], [0, 43], [0, 49], [0, 56], [0, 58], [0, 60], [0, 61], [0, 66], [0, 70], [0, 71], [0, 74], [0, 80], [0, 91], [0, 94], [0, 95], [0, 96], [0, 97], [0, 104], [0, ... | null | null | null | {"independent_set": [1, 16, 19, 33, 38, 40, 45, 64, 74, 80, 96, 98, 107, 114, 115, 124, 126, 138]} | 1 |
construct-mc-max-independent-set-l6-s4 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2843 edges:
(0,4), (0,8), (0,9), (0,10), (0,13), (0,19), (0,24), (0,25), (0,27), (0,34), (0,40), (0,41), (0,42), (0,48), (0,52), (0,56), (0,77), (0,85), (0,91), (0,99), (0,107), (0,126), (0,128), (0,132), (1,6), (1,10), (1,12), (1,14), (1,23), (1,25), (1,29), (1,30), (1,42)... | {"n": 140, "k": 18, "edges": [[0, 4], [0, 8], [0, 9], [0, 10], [0, 13], [0, 19], [0, 24], [0, 25], [0, 27], [0, 34], [0, 40], [0, 41], [0, 42], [0, 48], [0, 52], [0, 56], [0, 77], [0, 85], [0, 91], [0, 99], [0, 107], [0, 126], [0, 128], [0, 132], [1, 6], [1, 10], [1, 12], [1, 14], [1, 23], [1, 25], [1, 29], [1, 30], [1... | null | null | null | {"independent_set": [0, 3, 5, 11, 26, 28, 35, 38, 44, 58, 64, 75, 84, 94, 102, 113, 119, 130]} | 1 |
construct-mc-max-independent-set-l6-s5 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2760 edges:
(0,4), (0,5), (0,6), (0,7), (0,12), (0,16), (0,23), (0,26), (0,29), (0,31), (0,37), (0,38), (0,47), (0,58), (0,63), (0,71), (0,79), (0,81), (0,86), (0,90), (0,95), (0,101), (0,102), (0,103), (0,104), (0,106), (0,110), (0,111), (0,112), (0,113), (0,117), (0,119),... | {"n": 140, "k": 18, "edges": [[0, 4], [0, 5], [0, 6], [0, 7], [0, 12], [0, 16], [0, 23], [0, 26], [0, 29], [0, 31], [0, 37], [0, 38], [0, 47], [0, 58], [0, 63], [0, 71], [0, 79], [0, 81], [0, 86], [0, 90], [0, 95], [0, 101], [0, 102], [0, 103], [0, 104], [0, 106], [0, 110], [0, 111], [0, 112], [0, 113], [0, 117], [0, 1... | null | null | null | {"independent_set": [8, 16, 20, 24, 41, 54, 59, 66, 67, 69, 70, 76, 83, 92, 119, 120, 126, 127]} | 1 |
construct-mc-max-independent-set-l6-s6 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2842 edges:
(0,1), (0,3), (0,8), (0,13), (0,14), (0,19), (0,20), (0,23), (0,25), (0,34), (0,36), (0,42), (0,49), (0,51), (0,52), (0,54), (0,57), (0,62), (0,65), (0,69), (0,70), (0,71), (0,73), (0,78), (0,80), (0,82), (0,83), (0,85), (0,86), (0,94), (0,98), (0,102), (0,110),... | {"n": 140, "k": 18, "edges": [[0, 1], [0, 3], [0, 8], [0, 13], [0, 14], [0, 19], [0, 20], [0, 23], [0, 25], [0, 34], [0, 36], [0, 42], [0, 49], [0, 51], [0, 52], [0, 54], [0, 57], [0, 62], [0, 65], [0, 69], [0, 70], [0, 71], [0, 73], [0, 78], [0, 80], [0, 82], [0, 83], [0, 85], [0, 86], [0, 94], [0, 98], [0, 102], [0, ... | null | null | null | {"independent_set": [3, 16, 42, 44, 45, 46, 48, 71, 91, 93, 98, 100, 107, 108, 111, 120, 132, 136]} | 1 |
construct-mc-max-independent-set-l6-s7 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2828 edges:
(0,5), (0,9), (0,14), (0,16), (0,21), (0,29), (0,34), (0,37), (0,46), (0,47), (0,54), (0,56), (0,61), (0,68), (0,70), (0,71), (0,75), (0,77), (0,79), (0,86), (0,90), (0,96), (0,104), (0,108), (0,109), (0,124), (0,125), (0,126), (0,127), (0,129), (0,131), (0,133)... | {"n": 140, "k": 18, "edges": [[0, 5], [0, 9], [0, 14], [0, 16], [0, 21], [0, 29], [0, 34], [0, 37], [0, 46], [0, 47], [0, 54], [0, 56], [0, 61], [0, 68], [0, 70], [0, 71], [0, 75], [0, 77], [0, 79], [0, 86], [0, 90], [0, 96], [0, 104], [0, 108], [0, 109], [0, 124], [0, 125], [0, 126], [0, 127], [0, 129], [0, 131], [0, ... | null | null | null | {"independent_set": [10, 11, 20, 31, 39, 66, 67, 79, 87, 88, 96, 99, 103, 106, 111, 114, 121, 129]} | 1 |
construct-mc-max-independent-set-l6-s8 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2900 edges:
(0,1), (0,3), (0,4), (0,6), (0,8), (0,14), (0,15), (0,18), (0,19), (0,21), (0,24), (0,25), (0,30), (0,31), (0,41), (0,44), (0,45), (0,53), (0,55), (0,58), (0,67), (0,68), (0,71), (0,80), (0,81), (0,83), (0,84), (0,86), (0,103), (0,104), (0,106), (0,110), (0,112)... | {"n": 140, "k": 18, "edges": [[0, 1], [0, 3], [0, 4], [0, 6], [0, 8], [0, 14], [0, 15], [0, 18], [0, 19], [0, 21], [0, 24], [0, 25], [0, 30], [0, 31], [0, 41], [0, 44], [0, 45], [0, 53], [0, 55], [0, 58], [0, 67], [0, 68], [0, 71], [0, 80], [0, 81], [0, 83], [0, 84], [0, 86], [0, 103], [0, 104], [0, 106], [0, 110], [0,... | null | null | null | {"independent_set": [12, 20, 30, 32, 36, 45, 68, 70, 71, 80, 85, 97, 112, 114, 122, 124, 127, 136]} | 1 |
construct-mc-max-independent-set-l6-s9 | construct | mc_max_independent_set | graph_independent_set | graph_theory | competition | 6 | MathConstraint/max_independent_set | CC-BY-4.0 | [
"np_search"
] | Graph G with 140 vertices numbered 0..139 and 2920 edges:
(0,10), (0,14), (0,21), (0,24), (0,26), (0,27), (0,33), (0,34), (0,44), (0,50), (0,55), (0,56), (0,57), (0,65), (0,66), (0,69), (0,70), (0,71), (0,76), (0,81), (0,88), (0,93), (0,95), (0,96), (0,102), (0,103), (0,104), (0,106), (0,107), (0,109), (0,113), (0,115)... | {"n": 140, "k": 18, "edges": [[0, 10], [0, 14], [0, 21], [0, 24], [0, 26], [0, 27], [0, 33], [0, 34], [0, 44], [0, 50], [0, 55], [0, 56], [0, 57], [0, 65], [0, 66], [0, 69], [0, 70], [0, 71], [0, 76], [0, 81], [0, 88], [0, 93], [0, 95], [0, 96], [0, 102], [0, 103], [0, 104], [0, 106], [0, 107], [0, 109], [0, 113], [0, ... | null | null | null | {"independent_set": [9, 12, 24, 31, 46, 58, 71, 75, 90, 97, 106, 107, 109, 117, 126, 129, 133, 137]} | 1 |
construct-mc-non-transitive-dice-l1-s0 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 1 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 3 dice D_0, ..., D_2, each with 3 faces showing integers from 0..5 (values may repeat). Die D_i beats die D_j if, among the 9 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 4 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 3 for every i = 0..2.
Find such d... | {"n": 3, "m": 3, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[1, 1, 5], [0, 3, 4], [2, 2, 2]]} | 1 |
construct-mc-non-transitive-dice-l1-s1 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 1 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 3 dice D_0, ..., D_2, each with 4 faces showing integers from 0..7 (values may repeat). Die D_i beats die D_j if, among the 16 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 8 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 3 for every i = 0..2.
Find such ... | {"n": 3, "m": 4, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 4, 5, 5], [2, 3, 3, 7], [0, 2, 6, 6]]} | 1 |
construct-mc-non-transitive-dice-l2-s0 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 2 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 4 dice D_0, ..., D_3, each with 4 faces showing integers from 0..7 (values may repeat). Die D_i beats die D_j if, among the 16 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 8 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 4 for every i = 0..3.
Find such ... | {"n": 4, "m": 4, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[1, 2, 2, 7], [0, 1, 5, 5], [0, 4, 4, 4], [2, 3, 3, 6]]} | 1 |
construct-mc-non-transitive-dice-l2-s1 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 2 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 3 dice D_0, ..., D_2, each with 6 faces showing integers from 0..11 (values may repeat). Die D_i beats die D_j if, among the 36 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 18 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 3 for every i = 0..2.
Find suc... | {"n": 3, "m": 6, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 3, 4, 6, 10, 10], [1, 2, 5, 9, 9, 9], [4, 5, 7, 7, 8, 8]]} | 1 |
construct-mc-non-transitive-dice-l3-s0 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 3 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 4 dice D_0, ..., D_3, each with 6 faces showing integers from 0..11 (values may repeat). Die D_i beats die D_j if, among the 36 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 18 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 4 for every i = 0..3.
Find suc... | {"n": 4, "m": 6, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 5, 5, 6, 7, 7], [2, 3, 3, 5, 6, 11], [1, 2, 2, 5, 9, 11], [0, 0, 4, 8, 8, 9]]} | 1 |
construct-mc-non-transitive-dice-l3-s1 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 3 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 5 dice D_0, ..., D_4, each with 5 faces showing integers from 0..9 (values may repeat). Die D_i beats die D_j if, among the 25 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 12 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 5 for every i = 0..4.
Find such... | {"n": 5, "m": 5, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[2, 4, 5, 6, 9], [0, 4, 4, 6, 8], [2, 2, 3, 3, 8], [1, 1, 2, 9, 9], [0, 6, 6, 8, 8]]} | 1 |
construct-mc-non-transitive-dice-l4-s0 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 4 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 6 dice D_0, ..., D_5, each with 6 faces showing integers from 0..11 (values may repeat). Die D_i beats die D_j if, among the 36 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 18 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 6 for every i = 0..5.
Find suc... | {"n": 6, "m": 6, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[2, 5, 5, 5, 5, 11], [0, 0, 4, 9, 10, 11], [0, 4, 6, 8, 8, 8], [3, 3, 3, 6, 6, 11], [1, 1, 2, 10, 10, 11], [0, 6, 8, 8, 9, 9]]} | 1 |
construct-mc-non-transitive-dice-l4-s1 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 4 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 5 dice D_0, ..., D_4, each with 6 faces showing integers from 0..11 (values may repeat). Die D_i beats die D_j if, among the 36 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 18 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 5 for every i = 0..4.
Find suc... | {"n": 5, "m": 6, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 2, 2, 2, 2, 2], [1, 1, 1, 1, 6, 7], [0, 0, 1, 5, 5, 6], [0, 0, 1, 4, 4, 4], [0, 1, 1, 3, 3, 3]]} | 1 |
construct-mc-non-transitive-dice-l5-s0 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 5 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 6 dice D_0, ..., D_5, each with 7 faces showing integers from 0..13 (values may repeat). Die D_i beats die D_j if, among the 49 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 24 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 6 for every i = 0..5.
Find suc... | {"n": 6, "m": 7, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[1, 3, 4, 5, 5, 11, 12], [0, 2, 4, 4, 7, 8, 11], [0, 3, 5, 5, 6, 6, 7], [2, 3, 3, 4, 4, 12, 13], [0, 0, 3, 3, 10, 11, 13], [1, 2, 6, 7, 7, 8, 9]]} | 1 |
construct-mc-non-transitive-dice-l5-s1 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 5 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 5 dice D_0, ..., D_4, each with 7 faces showing integers from 0..13 (values may repeat). Die D_i beats die D_j if, among the 49 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 24 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 5 for every i = 0..4.
Find suc... | {"n": 5, "m": 7, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[2, 4, 6, 7, 8, 10, 12], [1, 4, 5, 6, 7, 10, 13], [2, 2, 3, 3, 6, 7, 13], [0, 1, 1, 5, 12, 12, 13], [0, 0, 9, 9, 10, 10, 12]]} | 1 |
construct-mc-non-transitive-dice-l5-s2 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 5 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 7 dice D_0, ..., D_6, each with 7 faces showing integers from 0..13 (values may repeat). Die D_i beats die D_j if, among the 49 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 24 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 7 for every i = 0..6.
Find suc... | {"n": 7, "m": 7, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 0, 1, 9, 9, 9, 10], [0, 5, 6, 6, 7, 8, 11], [1, 2, 2, 3, 10, 11, 13], [0, 1, 7, 7, 9, 9, 12], [0, 0, 5, 6, 10, 10, 11], [0, 2, 6, 6, 9, 9, 9], [3, 4, 5, 5, 7, 7, 12]]} | 1 |
construct-mc-non-transitive-dice-l6-s0 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 6 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 9 dice D_0, ..., D_8, each with 9 faces showing integers from 0..17 (values may repeat). Die D_i beats die D_j if, among the 81 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 40 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 9 for every i = 0..8.
Find suc... | {"n": 9, "m": 9, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 2, 4, 6, 7, 12, 12, 14, 15], [0, 4, 5, 9, 9, 10, 11, 11, 11], [0, 3, 3, 6, 8, 9, 10, 13, 16], [1, 1, 2, 6, 7, 11, 11, 12, 14], [0, 1, 4, 7, 9, 10, 10, 11, 12], [2, 4, 4, 4, 6, 8, 9, 9, 12], [0, 2, 3, 3, 3, 14, 15, 15, 15], [0, 2, 9, 9, 10, 12, 13, 14, 14], [2, 5, 6, 8, 8, 9, 13, 15, 16]]} | 1 |
construct-mc-non-transitive-dice-l6-s1 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 6 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 8 dice D_0, ..., D_7, each with 8 faces showing integers from 0..15 (values may repeat). Die D_i beats die D_j if, among the 64 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 32 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 8 for every i = 0..7.
Find suc... | {"n": 8, "m": 8, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[1, 3, 5, 5, 7, 9, 9, 15], [0, 1, 4, 6, 7, 7, 12, 12], [2, 4, 4, 5, 5, 5, 8, 15], [1, 1, 2, 3, 6, 14, 14, 15], [0, 0, 2, 8, 12, 12, 13, 13], [1, 5, 5, 5, 9, 10, 12, 12], [0, 1, 3, 4, 8, 13, 15, 15], [0, 1, 5, 6, 10, 10, 11, 12]]} | 1 |
construct-mc-non-transitive-dice-l6-s2 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 6 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 12 dice D_0, ..., D_11, each with 12 faces showing integers from 0..23 (values may repeat). Die D_i beats die D_j if, among the 144 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 72 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 12 for every i = 0..11.
Fi... | {"n": 12, "m": 12, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[0, 1, 6, 7, 7, 12, 14, 15, 15, 21, 22, 23], [2, 3, 5, 6, 10, 11, 12, 13, 19, 20, 21, 22], [0, 3, 6, 7, 9, 12, 13, 18, 18, 18, 18, 20], [0, 1, 2, 10, 11, 11, 13, 16, 16, 17, 19, 21], [0, 0, 6, 8, 10, 11, 11, 12, 12, 15, 20, 23], [3, 4, 6, 7, 7, 9, 9, 9, 15, 19, 20, 23], [1, 3, 5, 6, 6, 12, 13, 15, 15, 17, 17,... | 1 |
construct-mc-non-transitive-dice-l6-s3 | construct | mc_non_transitive_dice | intransitive_dice | probability | competition | 6 | MathConstraint/non_transitive_dice | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Design 10 dice D_0, ..., D_9, each with 10 faces showing integers from 0..19 (values may repeat). Die D_i beats die D_j if, among the 100 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 50 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 10 for every i = 0..9.
Find... | {"n": 10, "m": 10, "family": "mc_non_transitive_dice", "subset": "construct"} | null | null | null | {"dice": [[3, 4, 4, 5, 6, 8, 9, 10, 10, 19], [0, 2, 2, 3, 4, 6, 17, 18, 18, 19], [0, 0, 5, 5, 11, 12, 13, 15, 16, 17], [1, 3, 4, 10, 10, 11, 11, 11, 13, 15], [0, 2, 6, 6, 8, 8, 10, 16, 19, 19], [4, 4, 5, 6, 7, 9, 9, 10, 13, 14], [1, 2, 2, 2, 3, 13, 15, 16, 18, 18], [1, 1, 2, 3, 10, 11, 15, 15, 15, 15], [1, 3, 3, 3, 10,... | 1 |
construct-mc-number-partitioning-l1-s0 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 9 into 5 disjoint subsets (numbered 0..4) that all have the same sum 9 (the total is 45).
Find such a partition.
Answer format: {"x": [x_1, ..., x_9]}: a list of 9 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer as ... | {"n": 9, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s1 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 12 into 6 disjoint subsets (numbered 0..5) that all have the same sum 13 (the total is 78).
Find such a partition.
Answer format: {"x": [x_1, ..., x_12]}: a list of 12 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer... | {"n": 12, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s2 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 12 into 3 disjoint subsets (numbered 0..2) that all have the same sum 26 (the total is 78).
Find such a partition.
Answer format: {"x": [x_1, ..., x_12]}: a list of 12 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer... | {"n": 12, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s3 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 9 into 3 disjoint subsets (numbered 0..2) that all have the same sum 15 (the total is 45).
Find such a partition.
Answer format: {"x": [x_1, ..., x_9]}: a list of 9 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer as... | {"n": 9, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 1, 1, 0, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s4 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 8 into 3 disjoint subsets (numbered 0..2) that all have the same sum 12 (the total is 36).
Find such a partition.
Answer format: {"x": [x_1, ..., x_8]}: a list of 8 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer as... | {"n": 8, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [2, 1, 1, 0, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s5 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 11 into 6 disjoint subsets (numbered 0..5) that all have the same sum 11 (the total is 66).
Find such a partition.
Answer format: {"x": [x_1, ..., x_11]}: a list of 11 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer... | {"n": 11, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s6 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 11 into 3 disjoint subsets (numbered 0..2) that all have the same sum 22 (the total is 66).
Find such a partition.
Answer format: {"x": [x_1, ..., x_11]}: a list of 11 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer... | {"n": 11, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s7 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 10 into 5 disjoint subsets (numbered 0..4) that all have the same sum 11 (the total is 55).
Find such a partition.
Answer format: {"x": [x_1, ..., x_10]}: a list of 10 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer... | {"n": 10, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l1-s8 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 1 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 8 into 4 disjoint subsets (numbered 0..3) that all have the same sum 9 (the total is 36).
Find such a partition.
Answer format: {"x": [x_1, ..., x_8]}: a list of 8 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer as ... | {"n": 8, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s0 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 16 into 8 disjoint subsets (numbered 0..7) that all have the same sum 17 (the total is 136).
Find such a partition.
Answer format: {"x": [x_1, ..., x_16]}: a list of 16 integers in 0..7, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 16, "k": 8, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s1 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 15 into 6 disjoint subsets (numbered 0..5) that all have the same sum 20 (the total is 120).
Find such a partition.
Answer format: {"x": [x_1, ..., x_15]}: a list of 15 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 15, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [5, 4, 2, 2, 0, 1, 4, 3, 5, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s2 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 15 into 3 disjoint subsets (numbered 0..2) that all have the same sum 40 (the total is 120).
Find such a partition.
Answer format: {"x": [x_1, ..., x_15]}: a list of 15 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 15, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s3 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 15 into 4 disjoint subsets (numbered 0..3) that all have the same sum 30 (the total is 120).
Find such a partition.
Answer format: {"x": [x_1, ..., x_15]}: a list of 15 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 15, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s4 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 14 into 7 disjoint subsets (numbered 0..6) that all have the same sum 15 (the total is 105).
Find such a partition.
Answer format: {"x": [x_1, ..., x_14]}: a list of 14 integers in 0..6, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 14, "k": 7, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s5 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 15 into 5 disjoint subsets (numbered 0..4) that all have the same sum 24 (the total is 120).
Find such a partition.
Answer format: {"x": [x_1, ..., x_15]}: a list of 15 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 15, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 4, 1, 3, 1, 3, 0, 2, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s6 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 16 into 4 disjoint subsets (numbered 0..3) that all have the same sum 34 (the total is 136).
Find such a partition.
Answer format: {"x": [x_1, ..., x_16]}: a list of 16 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 16, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s7 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 15 into 8 disjoint subsets (numbered 0..7) that all have the same sum 15 (the total is 120).
Find such a partition.
Answer format: {"x": [x_1, ..., x_15]}: a list of 15 integers in 0..7, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 15, "k": 8, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s8 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 13 into 7 disjoint subsets (numbered 0..6) that all have the same sum 13 (the total is 91).
Find such a partition.
Answer format: {"x": [x_1, ..., x_13]}: a list of 13 integers in 0..6, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answer... | {"n": 13, "k": 7, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l2-s9 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 2 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 14 into 5 disjoint subsets (numbered 0..4) that all have the same sum 21 (the total is 105).
Find such a partition.
Answer format: {"x": [x_1, ..., x_14]}: a list of 14 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 14, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [2, 4, 1, 3, 1, 3, 0, 2, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l3-s0 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 25 into 5 disjoint subsets (numbered 0..4) that all have the same sum 65 (the total is 325).
Find such a partition.
Answer format: {"x": [x_1, ..., x_25]}: a list of 25 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 25, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 1, 1, 4, 1, 2, 1, 0, 0, 2, 0, 4, 2]} | 1 |
construct-mc-number-partitioning-l3-s1 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 24 into 5 disjoint subsets (numbered 0..4) that all have the same sum 60 (the total is 300).
Find such a partition.
Answer format: {"x": [x_1, ..., x_24]}: a list of 24 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 24, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 3, 4, 4, 2, 3, 3, 4, 2]} | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.