{
  "id": "1402.4754",
  "version": "v2",
  "published": "2014-02-19T18:18:16.000Z",
  "updated": "2016-02-04T22:43:44.000Z",
  "title": "Solution to a problem of Bollobás and Häggkvist on Hamilton cycles in regular graphs",
  "authors": [
    "Daniela Kühn",
    "Allan Lo",
    "Deryk Osthus",
    "Katherine Staden"
  ],
  "comment": "42 pages, to appear in JCTB",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that, for large $n$, every $3$-connected $D$-regular graph on $n$ vertices with $D \\geq n/4$ is Hamiltonian. This is best possible and confirms a conjecture posed independently by Bollob\\'as and H\\\"aggkvist in the 1970s. The proof builds on a structural decomposition result proved recently by the same authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-19T18:18:16.000Z",
      "comment": "41 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-04T22:43:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regular graph",
      "hamilton cycles",
      "structural decomposition result",
      "proof builds",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4754K"
    }
  }
}