{
  "id": "1012.2693",
  "version": "v2",
  "published": "2010-12-13T11:11:22.000Z",
  "updated": "2010-12-14T07:07:25.000Z",
  "title": "A solution to a conjecture on the rainbow connection number",
  "authors": [
    "Xiaolin Chen",
    "Xueliang Li"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G$, Chartrand et al. defined the rainbow connection number $rc(G)$ and the strong rainbow connection number $src(G)$ in \"G. Charand, G.L. John, K.A. Mckeon, P. Zhang, Rainbow connection in graphs, Mathematica Bohemica, 133(1)(2008) 85-98\". They raised the following conjecture: for two given positive $a$ and $b$, there exists a connected graph $G$ such that $rc(G)=a$ and $src(G)=b$ if and only if $a=b\\in\\{1,2\\}$ or $ 3\\leq a\\leq b$\". In this short note, we will show that the conjecture is true.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-14T07:07:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C40"
    ],
    "keywords": [
      "conjecture",
      "strong rainbow connection number",
      "mathematica bohemica",
      "short note",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.2693C"
    }
  }
}