{
  "id": "1110.5772",
  "version": "v1",
  "published": "2011-10-26T11:56:27.000Z",
  "updated": "2011-10-26T11:56:27.000Z",
  "title": "Rainbow connection number of dense graphs",
  "authors": [
    "Xueliang Li",
    "Mengmeng Liu",
    "Ingo Schiermeyer"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "An edge-colored graph $G$ is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In this paper we show that $rc(G)\\leq 3$, if $|E(G)|\\geq {{n-2}\\choose 2}+2$, and $rc(G)\\leq 4$, if $|E(G)|\\geq {{n-3}\\choose 2}+3$. These bounds are sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-26T11:56:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C40"
    ],
    "keywords": [
      "rainbow connection number",
      "dense graphs",
      "distinct colors",
      "smallest number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5772L"
    }
  }
}