{
  "id": "1310.6766",
  "version": "v1",
  "published": "2013-10-24T20:28:25.000Z",
  "updated": "2013-10-24T20:28:25.000Z",
  "title": "Extremal numbers for odd cycles",
  "authors": [
    "Zoltan Füredi",
    "David S. Gunderson"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We describe the C_{2k+1}-free graphs on n vertices with maximum number of edges. The extremal graphs are unique except for n = 3k-1, 3k, 4k-2, or 4k-1. The value of ex(n,C_{2k+1}) can be read out from the works of Bondy, Woodall, and Bollobas, but here we give a new streamlined proof. The complete determination of the extremal graphs is also new. We obtain that the bound for n_0(C_{2k+1}) is 4k in the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Turan graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-24T20:28:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05D99"
    ],
    "keywords": [
      "odd cycles",
      "extremal numbers",
      "bipartite turan graph",
      "unique extremal graph",
      "maximum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6766F"
    }
  }
}