{
  "id": "0709.1047",
  "version": "v3",
  "published": "2007-09-07T19:30:39.000Z",
  "updated": "2008-06-04T15:33:47.000Z",
  "title": "A Dirac type result on Hamilton cycles in oriented graphs",
  "authors": [
    "Luke Kelly",
    "Daniela Kühn",
    "Deryk Osthus"
  ],
  "comment": "Added an Ore-type result",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that for each \\alpha>0 every sufficiently large oriented graph G with \\delta^+(G),\\delta^-(G)\\ge 3|G|/8+ \\alpha |G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. In fact, we prove the stronger result that G is still Hamiltonian if \\delta(G)+\\delta^+(G)+\\delta^-(G)\\geq 3|G|/2 + \\alpha |G|. Up to the term \\alpha |G| this confirms a conjecture of H\\\"aggkvist. We also prove an Ore-type theorem for oriented graphs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-06-04T15:33:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C38",
      "05C45",
      "05C35"
    ],
    "keywords": [
      "dirac type result",
      "hamilton cycle",
      "sufficiently large oriented graph",
      "approximate solution",
      "stronger result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1047K"
    }
  }
}