{
  "id": "1111.6261",
  "version": "v2",
  "published": "2011-11-27T14:36:57.000Z",
  "updated": "2012-01-09T17:10:27.000Z",
  "title": "On the number of Hamilton cycles in pseudo-random graphs",
  "authors": [
    "Michael Krivelevich"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that if G is an (n,d,lambda)-graph (a d-regular graph on n vertices, all of whose non-trivial eigenvalues are at most lambda) and the following conditions are satisfied: 1. d/lambda >= (log n)^{1+epsilon} for some constant epsilon>0; 2.log d * lod (d/lambda) >> log n, then the number of Hamilton cycles in G is n!(d/n)^n(1+o(1))^n.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-09T17:10:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C80",
      "05C50"
    ],
    "keywords": [
      "hamilton cycles",
      "pseudo-random graphs",
      "non-trivial eigenvalues",
      "d-regular graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6261K"
    }
  }
}