{
  "id": "1010.6131",
  "version": "v1",
  "published": "2010-10-29T06:07:10.000Z",
  "updated": "2010-10-29T06:07:10.000Z",
  "title": "Rainbow connection in $3$-connected graphs",
  "authors": [
    "Xueliang Li",
    "Yongtang Shi"
  ],
  "comment": "7 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 by $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In this paper, we proved that $rc(G)\\leq 3(n+1)/5$ for all $3$-connected graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-29T06:07:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C40"
    ],
    "keywords": [
      "connected graph",
      "rainbow connection number",
      "smallest number",
      "distinct colors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.6131L"
    }
  }
}