File size: 1,723 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 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 | {
"name": "graceful_graph_k2_p6__v7_h",
"problem_type": "graceful_graph",
"params": {
"k": 2,
"p": 6
},
"prompt": "Find a graceful labeling for the graph G_{2,6}: 6 disjoint K_2 cliques (numbered 0 through 5), 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 12 vertices and 16 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 16 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 12 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.\n\nPartial assignment (fixed values that must be respected):\n- x[0]=6, x[3]=4\n- d[10]=11, d[14]=1, d[15]=12\nReturn a complete solution consistent with these fixed assignments.",
"satisfiable": true,
"solution": {
"x": [
6,
14,
9,
4,
5,
11,
16,
2,
0,
15,
1,
3
],
"d": [
8,
5,
6,
14,
15,
2,
3,
10,
4,
7,
11,
9,
16,
13,
1,
12
]
},
"difficulty": {
"solve_time_ms": 1225.8,
"search_space": 582622237229761,
"num_variables": 28,
"num_constraints": 20,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 79.14,
"solve_pct_type": 31.25
},
"partial_assignment": {
"x": {
"0": 6,
"3": 4
},
"d": {
"10": 11,
"14": 1,
"15": 12
}
}
} |