{
  "id": "0908.4572",
  "version": "v2",
  "published": "2009-08-31T16:21:29.000Z",
  "updated": "2013-07-07T09:06:59.000Z",
  "title": "Edge-disjoint Hamilton cycles in graphs",
  "authors": [
    "Demetres Christofides",
    "Daniela Kühn",
    "Deryk Osthus"
  ],
  "comment": "Minor Revision",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we give an approximate answer to a question of Nash-Williams from 1970: we show that for every \\alpha > 0, every sufficiently large graph on n vertices with minimum degree at least (1/2 + \\alpha)n contains at least n/8 edge-disjoint Hamilton cycles. More generally, we give an asymptotically best possible answer for the number of edge-disjoint Hamilton cycles that a graph G with minimum degree \\delta must have. We also prove an approximate version of another long-standing conjecture of Nash-Williams: we show that for every \\alpha > 0, every (almost) regular and sufficiently large graph on n vertices with minimum degree at least $(1/2 + \\alpha)n$ can be almost decomposed into edge-disjoint Hamilton cycles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-07T09:06:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C45",
      "05C70",
      "05D40"
    ],
    "keywords": [
      "edge-disjoint hamilton cycles",
      "minimum degree",
      "sufficiently large graph",
      "approximate answer",
      "nash-williams"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.4572C"
    }
  }
}