name stringlengths 14 134 | problem_type stringclasses 25
values | params dict | prompt stringlengths 167 1k | satisfiable bool 2
classes | solution dict | difficulty dict | partial_assignment dict |
|---|---|---|---|---|---|---|---|
pysms_min_degree_min_degree6_vertices10__v5_nh | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": 6,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices where the minimum degree is at least 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 83.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 45,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 27.26,
"solve_pct_type": 29.17
} | null |
pysms_min_degree_min_degree6_vertices13__v3_nh | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": 6,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 13 vertices where the minimum degree is at least 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 92.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 78,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 33.65,
"solve_pct_type": 70.83
} | null |
pysms_min_degree_min_degree6_vertices15__v6_nh | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": 6,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 15 vertices where the minimum degree is at least 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 95.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 105,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 36.65,
"solve_pct_type": 79.17
} | null |
pysms_min_girth_min_girth3_vertices10__v6_h | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 3,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices where the girth (shortest cycle length) is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (0,7), (0,4), (0,2), (2,9), (1,4), (4,... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 82.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 45,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 26.88,
"solve_pct_type": 29.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
4
],
[
0,
2
],
[
2,
9
],
[
1,
4
],
[
4,
6
],
[
2,
8
],
[
1,
8
],
[
... |
pysms_min_girth_min_girth3_vertices12__v1_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 3,
"vertices": 12,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 12 vertices where the girth (shortest cycle length) is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 87,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 66,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 28.76,
"solve_pct_type": 45.83
} | null |
pysms_min_girth_min_girth3_vertices17__v5_h | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 3,
"vertices": 17,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 17 vertices where the girth (shortest cycle length) is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 17, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (1,16), (5,15), (4,13), (2,7), (6,13),... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 99.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 136,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 40.79,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
16
],
[
5,
15
],
[
4,
13
],
[
2,
7
],
[
6,
13
],
[
8,
9
],
[
2,
6
],
[
8,
15
],
[
... |
pysms_min_girth_min_girth3_vertices9__v0_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 3,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the girth (shortest cycle length) is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 79.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 25,
"solve_pct_type": 20.83
} | null |
pysms_min_girth_min_girth4_vertices10__v4_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 4,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices where the girth (shortest cycle length) is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
9
],
[
1,
9
],
[
2,
9
],
[
3,
9
],
[
4,
9
],
[
5,
9
],
[
6,
9
],
[
7,
9
],
[
... | {
"solve_time_ms": 83.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 9,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 27.63,
"solve_pct_type": 37.5
} | null |
pysms_min_girth_min_girth4_vertices17__v9_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 4,
"vertices": 17,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 17 vertices where the girth (shortest cycle length) is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 17, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
16
],
[
1,
16
],
[
2,
16
],
[
3,
16
],
[
4,
16
],
[
5,
16
],
[
6,
16
],
[
7,
16
],
... | {
"solve_time_ms": 100.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 16,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 42.29,
"solve_pct_type": 70.83
} | null |
pysms_min_girth_min_girth6_vertices11__v3_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 11 vertices where the girth (shortest cycle length) is at least 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
1,
10
],
[
2,
10
],
[
3,
10
],
[
4,
10
],
[
5,
10
],
[
6,
10
],
[
7,
10
],
... | {
"solve_time_ms": 89,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 10,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 31.02,
"solve_pct_type": 54.17
} | null |
pysms_min_girth_min_girth6_vertices14__v2_h | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 14 vertices where the girth (shortest cycle length) is at least 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (9,13), (4,13)
Return a complete solut... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
13
],
[
1,
13
],
[
2,
13
],
[
3,
13
],
[
4,
13
],
[
5,
13
],
[
6,
13
],
[
7,
13
],
... | {
"solve_time_ms": 105.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 13,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 43.42,
"solve_pct_type": 79.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
9,
13
],
[
4,
13
]
],
"q": null
} |
pysms_min_girth_min_girth6_vertices8__v11_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 8 vertices where the girth (shortest cycle length) is at least 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
1,
7
],
[
2,
7
],
[
3,
7
],
[
4,
7
],
[
5,
7
],
[
6,
7
]
],
"q": null
} | {
"solve_time_ms": 32.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 7,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 16.73,
"solve_pct_type": 4.17
} | null |
pysms_min_girth_min_girth8_vertices14__v10_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 8,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 14 vertices where the girth (shortest cycle length) is at least 8.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
13
],
[
1,
13
],
[
2,
13
],
[
3,
13
],
[
4,
13
],
[
5,
13
],
[
6,
13
],
[
7,
13
],
... | {
"solve_time_ms": 860.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 13,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 56.2,
"solve_pct_type": 87.5
} | null |
pysms_min_girth_min_girth8_vertices16__v7_h | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 8,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 16 vertices where the girth (shortest cycle length) is at least 8.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (11,15), (3,15), (5,15)
Return a compl... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
15
],
[
1,
15
],
[
2,
15
],
[
3,
15
],
[
4,
15
],
[
5,
15
],
[
6,
15
],
[
7,
15
],
... | {
"solve_time_ms": 2528.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 15,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 93.42,
"solve_pct_type": 95.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
11,
15
],
[
3,
15
],
[
5,
15
]
],
"q": null
} |
pysms_min_girth_min_girth8_vertices9__v8_nh | pysms_min_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 8,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the girth (shortest cycle length) is at least 8.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
1,
8
],
[
2,
8
],
[
3,
8
],
[
4,
8
],
[
5,
8
],
[
6,
8
],
[
7,
8
]
],
"q": ... | {
"solve_time_ms": 72.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 8,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 24.62,
"solve_pct_type": 12.5
} | null |
pysms_mtf_vertices10__v8_nh | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 10 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
0,
9
],
[
1,
8
],
[
1,
9
],
[
2,
8
],
[
2,
9
],
[
3,
8
],
[
3,
9
],
[
... | {
"solve_time_ms": 90,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 16,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 31.95,
"solve_pct_type": 37.5
} | null |
pysms_mtf_vertices12__v1_nh | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 12 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
0,
11
],
[
1,
10
],
[
1,
11
],
[
2,
10
],
[
2,
11
],
[
3,
10
],
[
3,
11
],
... | {
"solve_time_ms": 94.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 20,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 35.9,
"solve_pct_type": 45.83
} | null |
pysms_mtf_vertices13__v0_nh | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 13 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
11
],
[
0,
12
],
[
1,
11
],
[
1,
12
],
[
2,
11
],
[
2,
12
],
[
3,
11
],
[
3,
12
],
... | {
"solve_time_ms": 96.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 22,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 37.22,
"solve_pct_type": 54.17
} | null |
pysms_mtf_vertices14__v4_nh | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 14 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
12
],
[
0,
13
],
[
1,
12
],
[
1,
13
],
[
2,
12
],
[
2,
13
],
[
3,
12
],
[
3,
13
],
... | {
"solve_time_ms": 100,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 24,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 41.92,
"solve_pct_type": 62.5
} | null |
pysms_mtf_vertices15__v6_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 15 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,14), (6,13), (7,13), (10,13), (6,14)
Return a complete solution con... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
13
],
[
0,
14
],
[
1,
13
],
[
1,
14
],
[
2,
13
],
[
2,
14
],
[
3,
13
],
[
3,
14
],
... | {
"solve_time_ms": 103.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 26,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 42.67,
"solve_pct_type": 70.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
14
],
[
6,
13
],
[
7,
13
],
[
10,
13
],
[
6,
14
]
],
"q": null
} |
pysms_mtf_vertices16__v7_nh | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 16 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
14
],
[
0,
15
],
[
1,
14
],
[
1,
15
],
[
2,
14
],
[
2,
15
],
[
3,
14
],
[
3,
15
],
... | {
"solve_time_ms": 105.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 28,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 43.8,
"solve_pct_type": 79.17
} | null |
pysms_mtf_vertices17__v3_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 17,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 17 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 17, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (0,15), (3,15), (6,15), (9,15), (11,15), (14,16)
Return a complete sol... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
15
],
[
0,
16
],
[
1,
15
],
[
1,
16
],
[
2,
15
],
[
2,
16
],
[
3,
15
],
[
3,
16
],
... | {
"solve_time_ms": 110.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 30,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 45.68,
"solve_pct_type": 87.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
15
],
[
3,
15
],
[
6,
15
],
[
9,
15
],
[
11,
15
],
[
14,
16
]
],
"q": null
} |
pysms_mtf_vertices20__v11_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 20,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a maximal triangle-free graph with 20 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 20, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (1,18), (4,18), (16,18), (4,19), (17,18), (11,19), (3,19)
Return a com... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
18
],
[
0,
19
],
[
1,
18
],
[
1,
19
],
[
2,
18
],
[
2,
19
],
[
3,
18
],
[
3,
19
],
... | {
"solve_time_ms": 118.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 46.43,
"solve_pct_type": 95.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
18
],
[
4,
18
],
[
16,
18
],
[
4,
19
],
[
17,
18
],
[
11,
19
],
[
3,
19
]
],
"q": null
} |
pysms_mtf_vertices6__v5_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 6,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Generate a maximal triangle-free graph with 6 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 6, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (3,5)
Return a complete solution consistent with these fixed assignments... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
1,
4
],
[
1,
5
],
[
2,
4
],
[
2,
5
],
[
3,
4
],
[
3,
5
]
],
"q": ... | {
"solve_time_ms": 7.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 8,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 0.19,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
3,
5
]
],
"q": null
} |
pysms_mtf_vertices7__v10_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 7,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Generate a maximal triangle-free graph with 7 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 7, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (0,6), (1,5)
Return a complete solution consistent with these fixed assi... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
5
],
[
0,
6
],
[
1,
5
],
[
1,
6
],
[
2,
5
],
[
2,
6
],
[
3,
5
],
[
3,
6
],
[
... | {
"solve_time_ms": 9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 10,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 2.82,
"solve_pct_type": 12.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
1,
5
]
],
"q": null
} |
pysms_mtf_vertices8__v9_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Generate a maximal triangle-free graph with 8 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (0,6), (2,6)
Return a complete solution consistent with these fixed assi... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
0,
7
],
[
1,
6
],
[
1,
7
],
[
2,
6
],
[
2,
7
],
[
3,
6
],
[
3,
7
],
[
... | {
"solve_time_ms": 9.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 12,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 3.76,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
2,
6
]
],
"q": null
} |
pysms_mtf_vertices9__v2_h | pysms_mtf | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Generate a maximal triangle-free graph with 9 vertices.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (4,7), (0,7)
Return a complete solution consistent with these fixed assi... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
1,
7
],
[
1,
8
],
[
2,
7
],
[
2,
8
],
[
3,
7
],
[
3,
8
],
[
... | {
"solve_time_ms": 21.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 14,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 11.84,
"solve_pct_type": 29.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
4,
7
],
[
0,
7
]
],
"q": null
} |
pysms_num_edges_bounds_max_edges16_min_edges11_vertices8__v6_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 11,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 16,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_n... | Generate a graph with 8 vertices where the number of edges is between 11 and 16.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
4
],
[
1,
5
],
[
1,
6
],
[
1,
7
],
[
... | {
"solve_time_ms": 16.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 16,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 8.46,
"solve_pct_type": 4.17
} | null |
pysms_num_edges_bounds_max_edges24_min_edges23_vertices11__v10_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 23,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 24,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 11 vertices where the number of edges is between 23 and 24.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
... | {
"solve_time_ms": 112.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 24,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 46.05,
"solve_pct_type": 62.5
} | null |
pysms_num_edges_bounds_max_edges30_min_edges21_vertices10__v9_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 21,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 30,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 10 vertices where the number of edges is between 21 and 30.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
1,
2
],
[
1,
3
],
[
1,
4
],
[
... | {
"solve_time_ms": 33.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 29,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 18.05,
"solve_pct_type": 12.5
} | null |
pysms_num_edges_bounds_max_edges31_min_edges27_vertices10__v4_h | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 27,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 31,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 10 vertices where the number of edges is between 27 and 31.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (4,8), (3,7), (6,7), (2,8), (0,8), (0,5)
Retu... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
1,
3
],
[
1,
4
],
[
... | {
"solve_time_ms": 49,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 31,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 23.12,
"solve_pct_type": 29.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
4,
8
],
[
3,
7
],
[
6,
7
],
[
2,
8
],
[
0,
8
],
[
0,
5
]
],
"q": null
} |
pysms_num_edges_bounds_max_edges33_min_edges33_vertices14__v7_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 33,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 33,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 14 vertices where the number of edges is between 33 and 33.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
... | {
"solve_time_ms": 104.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 33,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 43.05,
"solve_pct_type": 45.83
} | null |
pysms_num_edges_bounds_max_edges36_min_edges30_vertices11__v3_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 30,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 36,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 11 vertices where the number of edges is between 30 and 36.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
1,
3
],
[
1,
4
],
[
1,
5
],
[
1,
6
],
[
... | {
"solve_time_ms": 65.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 24.25,
"solve_pct_type": 37.5
} | null |
pysms_num_edges_bounds_max_edges37_min_edges28_vertices15__v1_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 28,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 37,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 15 vertices where the number of edges is between 28 and 37.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
... | {
"solve_time_ms": 106,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 37,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 44.17,
"solve_pct_type": 54.17
} | null |
pysms_num_edges_bounds_max_edges39_min_edges29_vertices13__v5_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 29,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 39,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 13 vertices where the number of edges is between 29 and 39.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
... | {
"solve_time_ms": 318,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 38,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 52.82,
"solve_pct_type": 95.83
} | null |
pysms_num_edges_bounds_max_edges40_min_edges14_vertices14__v2_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 14,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 40,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 14 vertices where the number of edges is between 14 and 40.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 227.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 40,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 51.32,
"solve_pct_type": 87.5
} | null |
pysms_num_edges_bounds_max_edges40_min_edges34_vertices18__v11_nh | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 34,
"min_girth": null,
"vertices": 18,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 40,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 18 vertices where the number of edges is between 34 and 40.
Return the graph as a list of edges (u, v) with 0 <= u < v < 18, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
... | {
"solve_time_ms": 143.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 40,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 47.56,
"solve_pct_type": 70.83
} | null |
pysms_num_edges_bounds_max_edges41_min_edges16_vertices14__v8_h | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 16,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 41,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 14 vertices where the number of edges is between 16 and 41.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,11), (1,5), (2,12), (2,4), (0,5), (3,7), (... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
... | {
"solve_time_ms": 220.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 41,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 50.94,
"solve_pct_type": 79.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
11
],
[
1,
5
],
[
2,
12
],
[
2,
4
],
[
0,
5
],
[
3,
7
],
[
2,
13
],
[
3,
13
]
],
"... |
pysms_num_edges_bounds_max_edges43_min_edges32_vertices11__v0_h | pysms_num_edges_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": 32,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": 43,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 11 vertices where the number of edges is between 32 and 43.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (1,9), (2,9), (6,9), (3,10), (5,7), (2,8), (7... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
1,
5
],
[
1,
6
],
[
1,
7
],
[
... | {
"solve_time_ms": 34.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 40,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 18.98,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
9
],
[
2,
9
],
[
6,
9
],
[
3,
10
],
[
5,
7
],
[
2,
8
],
[
7,
9
],
[
4,
6
]
],
"q":... |
queens_n11__v11_nh | queens | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 11 queens on a 11×11 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 11 integers where the i-th integer is the column position (0 to 10) of the queen in row i, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
9,
2,
4,
7,
10,
3,
6,
0,
5,
8,
1
]
} | {
"solve_time_ms": 1246.8,
"search_space": 285311670611,
"num_variables": 11,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 80.26,
"solve_pct_type": 54.17
} | null |
queens_n13__v1_h | queens | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 13 queens on a 13×13 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 13 integers where the i-th integer is the column position (0 to 12) of the queen in row i, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed value... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
4,
12,
3,
8,
6,
11,
9,
2,
0,
5,
7,
1,
10
]
} | {
"solve_time_ms": 1180.4,
"search_space": 302875106592253,
"num_variables": 13,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 78.38,
"solve_pct_type": 29.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": {
"1": 12,
"3": null,
"4": null,
"6": null,
"9": null,
"11": 1,
"12": null,
"16": null,
"18": null,
"21": null,
"26": null
}
} |
queens_n14__v7_h | queens | {
"n": 14,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 14 queens on a 14×14 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 14 integers where the i-th integer is the column position (0 to 13) of the queen in row i, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed value... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
10,
3,
11,
0,
4,
6,
1,
13,
7,
12,
8,
5,
2,
9
]
} | {
"solve_time_ms": 1143.3,
"search_space": 11112006825558016,
"num_variables": 14,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 78.01,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": {
"1": null,
"3": null,
"4": 4,
"6": 1,
"9": null,
"11": null,
"12": null,
"16": null,
"18": null,
"21": null,
"26": null
}
} |
queens_n21__v2_nh | queens | {
"n": 21,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 21 queens on a 21×21 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 21 integers where the i-th integer is the column position (0 to 20) of the queen in row i, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
20,
6,
8,
11,
7,
12,
15,
17,
19,
9,
2,
4,
1,
3,
16,
14,
10,
18,
13,
0,
5
]
} | {
"solve_time_ms": 1423.3,
"search_space": 5.842587018385982e+27,
"num_variables": 21,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 85.15,
"solve_pct_type": 79.17
} | null |
queens_n22__v0_h | queens | {
"n": 22,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 22 queens on a 22×22 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 22 integers where the i-th integer is the column position (0 to 21) of the queen in row i, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed value... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
17,
2,
4,
9,
0,
20,
10,
15,
19,
12,
1,
8,
6,
18,
21,
5,
14,
16,
11,
7,
3,
13
]
} | {
"solve_time_ms": 1416.6,
"search_space": 3.4142787736421956e+29,
"num_variables": 22,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 84.77,
"solve_pct_type": 70.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": {
"1": null,
"3": null,
"4": null,
"6": null,
"9": null,
"11": 8,
"12": null,
"16": 14,
"18": 11,
"21": 13,
"26": null
}
} |
queens_n26__v5_nh | queens | {
"n": 26,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 26 queens on a 26×26 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 26 integers where the i-th integer is the column position (0 to 25) of the queen in row i, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
24,
6,
8,
10,
12,
9,
16,
18,
21,
23,
25,
20,
0,
4,
7,
11,
3,
19,
2,
14,
17,
13,
1,
5,
22,
15
]
} | {
"solve_time_ms": 1471.4,
"search_space": 6.156119580207158e+36,
"num_variables": 26,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 87.03,
"solve_pct_type": 95.83
} | null |
queens_n27__v9_h | queens | {
"n": 27,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 27 queens on a 27×27 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 27 integers where the i-th integer is the column position (0 to 26) of the queen in row i, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed value... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
22,
9,
6,
18,
16,
0,
12,
17,
7,
23,
26,
3,
13,
4,
25,
8,
19,
11,
1,
15,
10,
21,
24,
20,
5,
2,
14
]
} | {
"solve_time_ms": 1461.1,
"search_space": 4.434264882430378e+38,
"num_variables": 27,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 86.65,
"solve_pct_type": 87.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": {
"1": null,
"3": null,
"4": null,
"6": null,
"9": 23,
"11": null,
"12": 13,
"16": null,
"18": 1,
"21": 21,
"26": 14
}
} |
queens_n4__v3_nh | queens | {
"n": 4,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 4 queens on a 4×4 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 4 integers where the i-th integer is the column position (0 to 3) of the queen in row i, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
2,
0,
3,
1
]
} | {
"solve_time_ms": 1316.1,
"search_space": 256,
"num_variables": 4,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 82.14,
"solve_pct_type": 62.5
} | null |
queens_n5__v4_h | queens | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 5 queens on a 5×5 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 5 integers where the i-th integer is the column position (0 to 4) of the queen in row i, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values tha... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
0,
2,
4,
1,
3
]
} | {
"solve_time_ms": 1241.1,
"search_space": 3125,
"num_variables": 5,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 79.89,
"solve_pct_type": 45.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": {
"1": 2,
"3": null,
"4": null,
"6": null,
"9": null,
"11": null,
"12": null,
"16": null,
"18": null,
"21": null,
"26": null
}
} |
queens_n7__v8_nh | queens | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 7 queens on a 7×7 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 7 integers where the i-th integer is the column position (0 to 6) of the queen in row i, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
0,
2,
4,
6,
1,
3,
5
]
} | {
"solve_time_ms": 1127.6,
"search_space": 823543,
"num_variables": 7,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 77.26,
"solve_pct_type": 12.5
} | null |
queens_n8__v10_nh | queens | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 8 queens on a 8×8 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 8 integers where the i-th integer is the column position (0 to 7) of the queen in row i, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
0,
5,
7,
2,
6,
3,
1,
4
]
} | {
"solve_time_ms": 1232.3,
"search_space": 16777216,
"num_variables": 8,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 79.51,
"solve_pct_type": 37.5
} | null |
queens_n9__v6_h | queens | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 9 queens on a 9×9 chessboard such that no two queens attack each other. Queens attack along rows, columns, and diagonals.
Return a list of 9 integers where the i-th integer is the column position (0 to 8) of the queen in row i, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values tha... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": [
0,
2,
6,
1,
7,
4,
8,
3,
5
]
} | {
"solve_time_ms": 1089.7,
"search_space": 387420489,
"num_variables": 9,
"num_constraints": 3,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 76.13,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": {
"1": null,
"3": 1,
"4": null,
"6": null,
"9": null,
"11": null,
"12": null,
"16": null,
"18": null,
"21": null,
"26": null
}
} |
ramsey_n12_r4_s4__v3_h | ramsey | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a 2-coloring of the edges of the complete graph K_12 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 4. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 66 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) f... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
1,
1,
0,
0,
0,
1,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
1,
0,
1,
0,
0,
1,
1,
... | {
"solve_time_ms": 1902.3,
"search_space": 73786976294838210000,
"num_variables": 66,
"num_constraints": 2970,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 91.54,
"solve_pct_type": 79.17
} | {
"x": null,
"d": null,
"seq": null,
"c": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": 0,
"8": null,
"9": 0,
"12": null,
"13": null,
"14": null,
"16": null,
"18": null,
"19": null,
"23": 1,
"27": 0,
... |
ramsey_n13_r4_s3__v4 | ramsey | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a 2-coloring of the edges of the complete graph K_13 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 78 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) f... | false | null | {
"solve_time_ms": 4319.4,
"search_space": 3.022314549036573e+23,
"num_variables": 78,
"num_constraints": 3003,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 96.8,
"solve_pct_type": 95.83
} | null |
ramsey_n13_r4_s4__v6_h | ramsey | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a 2-coloring of the edges of the complete graph K_13 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 4. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 78 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) f... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
1,
1,
1,
0,
1,
0,
1,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
0,
0,
1,
0,
0,
0,
0,
1,
0,
1,
0,
1,
0,
0,
1,
... | {
"solve_time_ms": 1899.5,
"search_space": 3.022314549036573e+23,
"num_variables": 78,
"num_constraints": 4290,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 91.17,
"solve_pct_type": 70.83
} | {
"x": null,
"d": null,
"seq": null,
"c": {
"0": null,
"1": null,
"2": null,
"3": 1,
"4": null,
"5": null,
"6": 0,
"7": null,
"8": null,
"9": null,
"12": null,
"13": 0,
"14": null,
"16": null,
"18": null,
"19": 0,
"23": null,
"27": 0,
"... |
ramsey_n5_r3_s3__v0_h | ramsey | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_5 such that there is no monochromatic red clique of size 3 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 10 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
0,
1,
1,
1,
0,
1,
1,
0,
0
],
"edges": null,
"q": null
} | {
"solve_time_ms": 935,
"search_space": 1024,
"num_variables": 10,
"num_constraints": 60,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 61.09,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": {
"0": null,
"1": null,
"2": null,
"3": 1,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": 0,
"12": null,
"13": null,
"14": null,
"16": null,
"18": null,
"19": null,
"23": null,
"27": nu... |
ramsey_n7_r3_s3__v1 | ramsey | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_7 such that there is no monochromatic red clique of size 3 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 21 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | false | null | {
"solve_time_ms": 919.9,
"search_space": 2097152,
"num_variables": 21,
"num_constraints": 210,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 58.83,
"solve_pct_type": 4.17
} | null |
ramsey_n7_r3_s4__v10_h | ramsey | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_7 such that there is no monochromatic red clique of size 3 and no monochromatic blue clique of size 4. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 21 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
1,
1,
0,
0,
1,
0,
1,
0,
1,
1,
0
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1117.2,
"search_space": 2097152,
"num_variables": 21,
"num_constraints": 210,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 76.88,
"solve_pct_type": 45.83
} | {
"x": null,
"d": null,
"seq": null,
"c": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": 1,
"8": 0,
"9": null,
"12": null,
"13": 0,
"14": 1,
"16": null,
"18": null,
"19": null,
"23": null,
"27": null,
... |
ramsey_n7_r4_s3__v9_h | ramsey | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_7 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 21 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
0,
0,
0,
1,
1,
1,
0,
0,
0,
1,
0,
0,
1,
0,
1,
0,
0,
0,
0,
0
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1283,
"search_space": 2097152,
"num_variables": 21,
"num_constraints": 210,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 81.39,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": null,
"c": {
"0": null,
"1": null,
"2": null,
"3": 0,
"4": null,
"5": null,
"6": null,
"7": 0,
"8": null,
"9": null,
"12": 0,
"13": null,
"14": null,
"16": null,
"18": 0,
"19": null,
"23": null,
"27": null,
... |
ramsey_n8_r3_s3__v2 | ramsey | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_8 such that there is no monochromatic red clique of size 3 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 28 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | false | null | {
"solve_time_ms": 930,
"search_space": 268435456,
"num_variables": 28,
"num_constraints": 336,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 60.34,
"solve_pct_type": 12.5
} | null |
ramsey_n8_r3_s4__v5_nh | ramsey | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_8 such that there is no monochromatic red clique of size 3 and no monochromatic blue clique of size 4. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 28 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
1,
1,
1,
0,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
0,
1,
0,
1,
0,
0,
1,
1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 950.4,
"search_space": 268435456,
"num_variables": 28,
"num_constraints": 378,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 62.59,
"solve_pct_type": 29.17
} | null |
ramsey_n8_r4_s3__v7_nh | ramsey | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_8 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 28 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
0,
0,
1,
1,
1,
0,
1,
0,
0,
0,
1,
0,
0,
0,
1,
0,
0,
1,
0,
0,
1,
0,
0,
0,
0,
1,
1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 988.7,
"search_space": 268435456,
"num_variables": 28,
"num_constraints": 378,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 68.98,
"solve_pct_type": 37.5
} | null |
ramsey_n8_r4_s4__v11_nh | ramsey | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_8 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 4. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 28 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | true | {
"x": null,
"d": null,
"seq": null,
"c": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
0,
0,
1,
1,
0,
0,
1,
0,
1,
0,
1,
1,
0
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1197.1,
"search_space": 268435456,
"num_variables": 28,
"num_constraints": 420,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 78.76,
"solve_pct_type": 54.17
} | null |
ramsey_n9_r4_s3__v8 | ramsey | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a 2-coloring of the edges of the complete graph K_9 such that there is no monochromatic red clique of size 4 and no monochromatic blue clique of size 3. Each edge is colored either 0 (red) or 1 (blue).
Return a list of 36 integers (0 or 1) representing the colors of edges listed in lexicographic order of (i,j) fo... | false | null | {
"solve_time_ms": 2735.2,
"search_space": 68719476736,
"num_variables": 36,
"num_constraints": 630,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 94.55,
"solve_pct_type": 87.5
} | null |
sudoku_n2__v1_h | sudoku | {
"n": 2,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Fill a Sudoku grid with block size 2 (so the full grid is 4x4, containing 4 rows, 4 columns, and 4 non-overlapping 2x2 blocks). Each row, column, and block must contain every integer from 1 to 4 exactly once.
Return a list of 16 integers (the grid in row-major order: cell at row i, column j is at index i*4+j), or stat... | true | {
"x": [
1,
2,
3,
4,
3,
4,
1,
2,
2,
1,
4,
3,
4,
3,
2,
1
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1036.2,
"search_space": 4294967296,
"num_variables": 16,
"num_constraints": 18,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 73.5,
"solve_pct_type": 50
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": 2,
"8": null,
"9": 1,
"10": null,
"11": null,
"12": 4,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"21"... |
sudoku_n3__v0_h | sudoku | {
"n": 3,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Fill a Sudoku grid with block size 3 (so the full grid is 9x9, containing 9 rows, 9 columns, and 9 non-overlapping 3x3 blocks). Each row, column, and block must contain every integer from 1 to 9 exactly once.
Return a list of 81 integers (the grid in row-major order: cell at row i, column j is at index i*9+j), or stat... | true | {
"x": [
1,
2,
3,
4,
5,
6,
7,
8,
9,
4,
5,
6,
7,
8,
9,
1,
2,
3,
7,
8,
9,
1,
2,
3,
4,
5,
6,
2,
1,
4,
3,
6,
5,
8,
9,
7,
3,
6,
5,
8,
9,
7,
2,
1,
... | {
"solve_time_ms": 988.4,
"search_space": 1.9662705047555292e+77,
"num_variables": 81,
"num_constraints": 33,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 68.61,
"solve_pct_type": 16.67
} | {
"x": {
"0": null,
"1": null,
"2": 3,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": 6,
"12": null,
"13": 8,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": 9,
"21": n... |
sudoku_n4__v2_h | sudoku | {
"n": 4,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Fill a Sudoku grid with block size 4 (so the full grid is 16x16, containing 16 rows, 16 columns, and 16 non-overlapping 4x4 blocks). Each row, column, and block must contain every integer from 1 to 16 exactly once.
Return a list of 256 integers (the grid in row-major order: cell at row i, column j is at index i*16+j),... | true | {
"x": [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
5,
6,
7,
8,
1,
2,
3,
4,
13,
14,
15,
16,
9,
10,
11,
12,
9,
10,
11,
12,
13,
14,
15,
16,
1,
... | {
"solve_time_ms": 1267,
"search_space": null,
"num_variables": 256,
"num_constraints": 54,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 81.02,
"solve_pct_type": 83.33
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": 6,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": 14,
"14": 15,
"15": null,
"17": null,
"18": 7,
"19": null,
"20": null,
"21":... |
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