File size: 1,584 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 67 68 69 70 | {
"name": "graceful_graph_k3_p5__v2_nh",
"problem_type": "graceful_graph",
"params": {
"k": 3,
"p": 5
},
"prompt": "Find a graceful labeling for the graph G_{3,5}: 5 disjoint K_3 cliques (numbered 0 through 4), where each pair of consecutive cliques (g, g+1) is connected by 3 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..2. The graph has 15 vertices and 27 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 27 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 15 integers giving the vertex labels, ordered by clique then vertex within clique (so the i-th block of 3 consecutive entries gives the labels for clique i), or state \"UNSATISFIABLE\" if no such labeling exists.",
"satisfiable": true,
"solution": {
"x": [
5,
24,
14,
23,
3,
7,
1,
6,
18,
25,
12,
26,
2,
27,
0
],
"d": [
19,
9,
10,
20,
16,
4,
5,
17,
12,
13,
1,
14,
25,
2,
27,
18,
21,
7,
22,
3,
11,
24,
6,
8,
23,
15,
26
]
},
"difficulty": {
"solve_time_ms": 1655.4,
"search_space": 5097655355238390956032,
"num_variables": 42,
"num_constraints": 31,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 88.91,
"solve_pct_type": 81.25
},
"partial_assignment": null
} |