{
  "id": "2011.04255",
  "version": "v1",
  "published": "2020-11-09T09:03:40.000Z",
  "updated": "2020-11-09T09:03:40.000Z",
  "title": "Total domination in plane triangulations",
  "authors": [
    "M. Claverol",
    "A. García",
    "G. Hernández",
    "C. Hernando",
    "M. Maureso",
    "M. Mora",
    "J. Tejel"
  ],
  "categories": [
    "math.CO",
    "cs.CG"
  ],
  "abstract": "A total dominating set of a graph $G=(V,E)$ is a subset $D$ of $V$ such that every vertex in $V$ is adjacent to at least one vertex in $D$. The total domination number of $G$, denoted by $\\gamma _t (G)$, is the minimum cardinality of a total dominating set of $G$. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that $\\gamma _t (G) \\le \\lfloor \\frac{2n}{5}\\rfloor$ for any near-triangulation $G$ of order $n\\ge 5$, with two exceptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-09T09:03:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane triangulations",
      "total dominating set",
      "total domination number",
      "minimum cardinality",
      "near-triangulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}