File size: 1,329 Bytes
a9e7957 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | {
"name": "graceful_graph_k2_p4__v6_nh",
"problem_type": "graceful_graph",
"params": {
"k": 2,
"p": 4
},
"prompt": "Find a graceful labeling for the graph G_{2,4}: 4 disjoint K_2 cliques (numbered 0 through 3), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 8 vertices and 10 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 10 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 8 integers giving the vertex labels, ordered by clique then vertex within clique (so the i-th block of 2 consecutive entries gives the labels for clique i), or state \"UNSATISFIABLE\" if no such labeling exists.",
"satisfiable": true,
"solution": {
"x": [
0,
2,
10,
3,
1,
7,
9,
4
],
"d": [
2,
7,
6,
5,
10,
1,
9,
4,
8,
3
]
},
"difficulty": {
"solve_time_ms": 1359.6,
"search_space": 214358881,
"num_variables": 18,
"num_constraints": 14,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 83.65,
"solve_pct_type": 56.25
},
"partial_assignment": null
} |