{
  "id": "1705.03096",
  "version": "v1",
  "published": "2017-05-08T21:32:44.000Z",
  "updated": "2017-05-08T21:32:44.000Z",
  "title": "Partial Domination in Graphs",
  "authors": [
    "Benjamin M. Case",
    "Stephen T. Hedetniemi",
    "Renu C. Laskar",
    "Drew J. Lipman"
  ],
  "comment": "First presented at the 48th Southeastern International Conference on Combinatorics, Graph Theory & Computing March 6-10, 2017",
  "categories": [
    "math.CO"
  ],
  "abstract": "A set $S\\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $\\gamma(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a set $S$ is a $\\gamma$-set. The single greatest focus of research in domination theory is the determination of the value of $\\gamma(G)$. By definition, all vertices must be dominated by a $\\gamma$-set. In this paper we propose relaxing this requirement, by seeking sets of vertices that dominate a prescribed fraction of the vertices of a graph. We focus particular attention on $1/2$ domination, that is, sets of vertices that dominate at least half of the vertices of a graph $G$. Keywords: partial domination, dominating set, partial domination number, domination number",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-08T21:32:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dominating set",
      "partial domination number",
      "single greatest focus",
      "domination theory",
      "minimum cardinality"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}