{
  "id": "1204.4298",
  "version": "v3",
  "published": "2012-04-19T09:42:36.000Z",
  "updated": "2013-04-03T09:33:32.000Z",
  "title": "Rainbow connection number and independence number of a graph",
  "authors": [
    "Jiuying Dong",
    "Xueliang Li"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be an edge-colored connected graph. A path of $G$ is called rainbow if its every edge is colored by a distinct color. $G$ is called rainbow connected if there exists a rainbow path between every two vertices of $G$. The minimum number of colors that are needed to make $G$ rainbow connected is called the rainbow connection number of $G$, denoted by $rc(G)$. In this paper, we investigate the relation between the rainbow connection number and the independence number of a graph. We show that if $G$ is a connected graph, then $rc(G)\\leq 2\\alpha(G)-1$. Two examples $G$ are given to show that the upper bound $2\\alpha(G)-1$ is equal to the diameter of $G$, and therefore the best possible since the diameter is a lower bound of $rc(G)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-03T09:33:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C40",
      "05C69"
    ],
    "keywords": [
      "rainbow connection number",
      "independence number",
      "connected graph",
      "lower bound",
      "distinct color"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4298D"
    }
  }
}