{
  "name": "graceful_graph_k3_p6__v4_nh",
  "problem_type": "graceful_graph",
  "params": {
    "k": 3,
    "p": 6
  },
  "prompt": "Find a graceful labeling for the graph G_{3,6}: 6 disjoint K_3 cliques (numbered 0 through 5), 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 18 vertices and 33 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 33 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 18 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": [
      1,
      2,
      32,
      33,
      20,
      5,
      0,
      29,
      3,
      4,
      10,
      26,
      9,
      30,
      19,
      23,
      6,
      31
    ],
    "d": [
      1,
      31,
      30,
      13,
      28,
      15,
      29,
      3,
      26,
      6,
      22,
      16,
      21,
      10,
      11,
      17,
      8,
      25,
      32,
      18,
      27,
      33,
      9,
      2,
      4,
      19,
      23,
      5,
      20,
      7,
      14,
      24,
      12
    ]
  },
  "difficulty": {
    "solve_time_ms": 1860.4,
    "search_space": 3686553210602841700043063296,
    "num_variables": 51,
    "num_constraints": 37,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 90.41,
    "solve_pct_type": 93.75
  },
  "partial_assignment": null
}