{
  "id": "1207.2748",
  "version": "v1",
  "published": "2012-07-11T19:13:08.000Z",
  "updated": "2012-07-11T19:13:08.000Z",
  "title": "On the number of Hamilton cycles in sparse random graphs",
  "authors": [
    "R. Glebov",
    "M. Krivelevich"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove that the number of Hamilton cycles in the random graph G(n,p) is n!p^n(1+o(1))^n a.a.s., provided that p\\geq (ln n+ln ln n+\\omega(1))/n. Furthermore, we prove the hitting-time version of this statement, showing that in the random graph process, the edge that creates a graph of minimum degree 2 creates (ln n/e)^n(1+o(1))^n Hamilton cycles a.a.s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-11T19:13:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C45",
      "05D40",
      "05C20",
      "05C35"
    ],
    "keywords": [
      "sparse random graphs",
      "hamilton cycles",
      "random graph process",
      "hitting-time version",
      "minimum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2748G"
    }
  }
}