{
  "id": "1108.2871",
  "version": "v2",
  "published": "2011-08-14T13:41:26.000Z",
  "updated": "2012-04-23T16:28:49.000Z",
  "title": "A bound for the number of vertices of a polytope with applications",
  "authors": [
    "Alexander Barvinok"
  ],
  "comment": "9 pages, various improvements",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "We prove that the number of vertices of a polytope of a particular kind is exponentially large in the dimension of the polytope. As a corollary, we prove that an n-dimensional centrally symmetric polytope with O(n) facets has 2^{Omega(n)} vertices and that the number of r-factors in a k-regular graph is exponentially large in the number of vertices of the graph provided k >2r and every cut in the graph with at least two vertices on each side has more than k/r edges.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-23T16:28:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B12",
      "05A16",
      "05C70",
      "05C30"
    ],
    "keywords": [
      "applications",
      "n-dimensional centrally symmetric polytope",
      "exponentially large",
      "k-regular graph",
      "k/r edges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2871B"
    }
  }
}