{
  "id": "1109.0707",
  "version": "v2",
  "published": "2011-09-04T12:07:25.000Z",
  "updated": "2011-09-16T17:23:49.000Z",
  "title": "A brief, simple proof of Vizing's conjecture",
  "authors": [
    "Elliot Krop"
  ],
  "comment": "This paper has been withdrawn by the author due to a problem with the \"label exchange\"",
  "categories": [
    "math.CO"
  ],
  "abstract": "For any graph $G=(V,E)$, a subset $S\\subseteq V$ \\emph{dominates} $G$ if all vertices are contained in the closed neighborhood of $S$, that is $N[S]=V$. The minimum cardinality over all such $S$ is called the domination number, written $\\gamma(G)$. In 1963, V.G. Vizing conjectured that $\\gamma(G \\square H) \\geq \\gamma(G)\\gamma(H)$ where $\\square$ stands for the Cartesian product of graphs. In this note, we prove the conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-16T17:23:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple proof",
      "vizings conjecture",
      "cartesian product",
      "minimum cardinality",
      "domination number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0707K"
    }
  }
}