{
  "id": "math/0512493",
  "version": "v1",
  "published": "2005-12-21T14:54:21.000Z",
  "updated": "2005-12-21T14:54:21.000Z",
  "title": "A counterexample to a conjecture of Laurent and Poljak",
  "authors": [
    "Antoine Deza",
    "Gabriel Indik"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The metric polytope m(n) is the polyhedron associated with all semimetrics on n nodes. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n<9 and, in particular, for the 1 550 825 600 vertices of m(8). While the overwhelming majority of the known vertices of m(9) satisfy the Laurent-Poljak conjecture, we exhibit a fractional vertex not adjacent to any integral vertex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-21T14:54:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C27",
      "52B12"
    ],
    "keywords": [
      "counterexample",
      "metric polytope",
      "integral vertex",
      "fractional vertex",
      "conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12493D"
    }
  }
}