{
  "id": "1308.0269",
  "version": "v2",
  "published": "2013-08-01T17:17:26.000Z",
  "updated": "2014-12-10T22:44:27.000Z",
  "title": "Semi-degree threshold for anti-directed Hamiltonian cycles",
  "authors": [
    "Louis DeBiasio",
    "Theodore Molla"
  ],
  "comment": "20 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1960, Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if D is a directed graph on n vertices with minimum out-degree and in-degree at least n/2 (i.e. minimum semi-degree at least n/2), then D contains a directed Hamiltonian cycle. Of course there are other orientations of a cycle in a directed graph and it is not clear that the semi-degree threshold for the directed Hamiltonian cycle is the same as the semi-degree threshold for some other orientation. In 1980, Grant initiated the problem of determining the minimum semi-degree threshold for the anti-directed Hamiltonian cycle (an orientation in which consecutive edges alternate direction). We prove that for sufficiently large even n, if D is a directed graph on n vertices with minimum semi-degree at least n/2+1, then D contains an anti-directed Hamiltonian cycle. This result is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-01T17:17:26.000Z",
      "comment": "18 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-10T22:44:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anti-directed hamiltonian cycle",
      "directed graph",
      "minimum semi-degree threshold",
      "orientation",
      "consecutive edges alternate direction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0269D"
    }
  }
}