files / problems / kissing-5d / compute / q7 / star_cover_min.json

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{
  "n_four_star_unions": 210,
  "four_star_union_sizes": [
    26,
    27,
    28
  ],
  "n_five_star_unions": 252,
  "five_star_union_sizes": [
    30,
    31,
    32
  ],
  "min_star_cover_5": 5,
  "witness_cover_5": [
    12,
    15,
    19,
    21,
    28
  ],
  "bounds_cover_5": [
    {
      "bound": 6,
      "sat": true
    },
    {
      "bound": 3,
      "sat": false
    },
    {
      "bound": 4,
      "sat": false
    },
    {
      "bound": 5,
      "sat": true
    }
  ],
  "min_star_cover_6": 8,
  "witness_cover_6": [
    13,
    14,
    16,
    19,
    21,
    22,
    29,
    30
  ],
  "bounds_cover_6": [
    {
      "bound": 6,
      "sat": false
    },
    {
      "bound": 9,
      "sat": true
    },
    {
      "bound": 7,
      "sat": false
    },
    {
      "bound": 8,
      "sat": true
    }
  ],
  "k19_empty_by_cover_5": false,
  "k19_empty_by_cover_6": false,
  "found_41": false,
  "comment": "min |U| with star-cover >= 5 (resp. 6) is the min hitting set of 4-star (resp. 5-star) complements.  Neither empties |U|=19 by combinatorics."
}