{
  "id": "1105.4210",
  "version": "v2",
  "published": "2011-05-21T03:20:39.000Z",
  "updated": "2011-05-26T08:18:40.000Z",
  "title": "Sharp upper bound for the rainbow connection numbers of 2-connected graphs",
  "authors": [
    "Xueliang Li",
    "Sujuan Liu"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "An edge-colored graph $G$, where adjacent edges may be colored the same, is rainbow connected if any two vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of a connected graph $G$ is the smallest number of colors that are needed in order to make $G$ rainbow connected. In this paper, we give a sharp upper bound that $rc(G)\\leq\\lceil\\frac{n}{2}\\rceil$ for any 2-connected graph $G$ of order $n$, which improves the results of Caro et al. to best possible.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-26T08:18:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C40"
    ],
    "keywords": [
      "sharp upper bound",
      "rainbow connection number",
      "adjacent edges",
      "distinct colors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.4210L"
    }
  }
}