files / problems / kissing-5d / compute / q5 / t5_degeneracy.json

3.4 KB · on GitHub

{
  "n": 355,
  "m": 52419,
  "degree": {
    "min": 249,
    "max": 346,
    "mean": 295.3183098591549,
    "mean_exact": "104838/355",
    "histogram": {
      "249": 6,
      "253": 12,
      "257": 6,
      "258": 2,
      "268": 12,
      "272": 6,
      "274": 12,
      "275": 6,
      "278": 12,
      "279": 12,
      "280": 12,
      "281": 12,
      "285": 12,
      "286": 6,
      "287": 18,
      "288": 14,
      "290": 3,
      "291": 12,
      "292": 6,
      "293": 6,
      "296": 6,
      "297": 12,
      "298": 5,
      "301": 18,
      "305": 12,
      "307": 6,
      "310": 2,
      "313": 12,
      "314": 9,
      "316": 6,
      "319": 6,
      "320": 18,
      "322": 18,
      "326": 18,
      "328": 2,
      "330": 9,
      "332": 6,
      "346": 3
    }
  },
  "degeneracy": 260,
  "elim_degree_max": 260,
  "core_check_ok": true,
  "core_histogram": {
    "249": 6,
    "253": 12,
    "257": 8,
    "260": 329
  },
  "published": {
    "D5": {
      "remainder_size": 35,
      "is_35_clique": true
    },
    "L5": {
      "remainder_size": 35,
      "is_35_clique": true
    },
    "Q5": {
      "remainder_size": 35,
      "is_35_clique": true
    },
    "R5": {
      "remainder_size": 35,
      "is_35_clique": true
    }
  },
  "published_intersections": {
    "pairwise": {
      "D5&L5": 27,
      "D5&Q5": 25,
      "D5&R5": 21,
      "L5&Q5": 21,
      "L5&R5": 25,
      "Q5&R5": 31
    },
    "triple": {
      "D5&L5&Q5": 21,
      "D5&L5&R5": 21,
      "D5&Q5&R5": 21,
      "L5&Q5&R5": 21
    },
    "D5&L5&Q5&R5": 21
  },
  "in_how_many_published_35": {
    "0": 302,
    "1": 8,
    "2": 24,
    "3": 0,
    "4": 21
  },
  "union_of_published_35": 53,
  "smallest_last_colors": 55,
  "colouring": {
    "ncolors_attempt": 36,
    "found_36": false,
    "found_35": false,
    "method": null,
    "colors_used": null,
    "colouring": null,
    "attempts": [
      {
        "method": "smallest_last_unlimited",
        "colors_used": 55
      },
      {
        "method": "smallest_last_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "largest_degree_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "smallest_degree_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "natural_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "dsatur_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_D5_dsatur_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_D5_sl_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_L5_dsatur_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_L5_sl_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_Q5_dsatur_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_Q5_sl_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_R5_dsatur_36",
        "ok": false,
        "ncolors": 36
      },
      {
        "method": "precolour_R5_sl_36",
        "ok": false,
        "ncolors": 36
      }
    ]
  },
  "comment": "No 35- or 36-colouring from the greedy / DSATUR / degeneracy-order attempts.  Incomplete search, not a lower bound on chi.  A d-degenerate graph is (d+1)-colourable; here d = 260.  Did not claim tau_5 = 40."
}