{
  "name": "graceful_graph_k2_p5__v1_nh",
  "problem_type": "graceful_graph",
  "params": {
    "k": 2,
    "p": 5
  },
  "prompt": "Find a graceful labeling for the graph G_{2,5}: 5 disjoint K_2 cliques (numbered 0 through 4), 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 10 vertices and 13 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 13 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 10 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": [
      11,
      6,
      4,
      10,
      1,
      2,
      12,
      0,
      3,
      13
    ],
    "d": [
      5,
      6,
      1,
      12,
      10,
      7,
      4,
      3,
      8,
      11,
      2,
      9,
      13
    ]
  },
  "difficulty": {
    "solve_time_ms": 1003.9,
    "search_space": 289254654976,
    "num_variables": 23,
    "num_constraints": 17,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 70.49,
    "solve_pct_type": 6.25
  },
  "partial_assignment": null
}