{
  "id": "1510.00511",
  "version": "v1",
  "published": "2015-10-02T07:43:36.000Z",
  "updated": "2015-10-02T07:43:36.000Z",
  "title": "Simple polytopes without small separators",
  "authors": [
    "Lauri Loiskekoski",
    "Günter M. Ziegler"
  ],
  "comment": "7 pages",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "We show that by cutting off the vertices and then the edges of neighborly cubical polytopes, one obtains simple 4-dimensional polytopes with n vertices such that all separators of the graph have size at least $\\Omega(n/\\log^{3/2}n)$. This disproves a conjecture by Kalai from 1991/2004.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-02T07:43:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "52B11",
      "05C12",
      "05C40"
    ],
    "keywords": [
      "small separators",
      "simple polytopes",
      "neighborly cubical polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000511L"
    }
  }
}