{
  "id": "1804.00158",
  "version": "v2",
  "published": "2018-03-31T10:58:08.000Z",
  "updated": "2018-04-11T07:35:30.000Z",
  "title": "On the maximum number of minimum dominating sets in forests",
  "authors": [
    "J. D. Alvarado",
    "S. Dantas",
    "E. Mohr",
    "D. Rautenbach"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number $\\gamma$ has at most $2^\\gamma$ minimum dominating sets. Bien gave a counterexample, which allows to construct forests with domination number $\\gamma$ and $2.0598^\\gamma$ minimum dominating sets. We show that every forest with domination number $\\gamma$ has at most $2.4606^\\gamma$ minimum dominating sets, and that every tree with independence number $\\alpha$ has at most $2^{\\alpha-1}+1$ maximum independent sets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-04-11T07:35:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum dominating sets",
      "maximum number",
      "domination number",
      "maximum independent sets",
      "hedetniemi"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}