{
  "id": "1310.5634",
  "version": "v2",
  "published": "2013-10-21T16:37:21.000Z",
  "updated": "2014-07-31T12:10:42.000Z",
  "title": "Upper bounds on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges",
  "authors": [
    "M. Aaghabali",
    "S. Akbari",
    "S. Friedland",
    "K. Markstrom",
    "Z. Tajfirouz"
  ],
  "comment": "17 pages, 2 tables, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on 2n vertices. The upper bound is sharp for n even. For n odd we state a conjecture on a sharp upper bound.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-31T12:10:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "05C20",
      "05C70"
    ],
    "keywords": [
      "perfect matchings",
      "directed complete bipartite balanced graph",
      "sharp upper bound",
      "simple graphs",
      "2n vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5634A"
    }
  }
}