{
  "id": "0803.0864",
  "version": "v1",
  "published": "2008-03-06T13:44:47.000Z",
  "updated": "2008-03-06T13:44:47.000Z",
  "title": "An upper bound for the number of perfect matchings in graphs",
  "authors": [
    "Shmuel Friedland"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO",
    "math.HO"
  ],
  "abstract": "We give an upper bound on the number of perfect matchings in an undirected simple graph $G$ with an even number of vertices, in terms of the degrees of all the vertices in $G$. This bound is sharp if $G$ is a union of complete bipartite graphs. This bound is a generalization of the upper bound on the number of perfect matchings in bipartite graphs on $n+n$ vertices given by the Bregman-Minc inequality for the permanents of $(0,1)$ matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-06T13:44:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05C70"
    ],
    "keywords": [
      "perfect matchings",
      "upper bound",
      "complete bipartite graphs",
      "undirected simple graph",
      "bregman-minc inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0864F"
    }
  }
}