{
  "id": "0907.2421",
  "version": "v2",
  "published": "2009-07-14T18:17:25.000Z",
  "updated": "2010-09-15T02:12:45.000Z",
  "title": "Complete Minors, Independent Sets, and Chordal Graphs",
  "authors": [
    "Jozsef Balogh",
    "John Lenz",
    "Hehui Wu"
  ],
  "journal": "Discuss. Math. Graph Theory. vol 31(4). 2011. 639-674",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conjecture states that h(G) >= \\chi(G). Since \\chi(G) \\alpha(G) >= |V(G)|, Hadwiger's Conjecture implies that \\alpha(G) h(G) >= |V(G)|. We show that (2 \\alpha(G) - \\lceil log_t(t \\alpha(G)/2) \\rceil) h(G) \\geq |V(G)| where t is approximately 6.83. For graphs with \\alpha(G) \\geq 14, this improves on a recent result of Kawarabayashi and Song who showed (2 \\alpha(G) - 2) h(G) >= |V(G)| when \\alpha(G) >= 3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-15T02:12:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete minor",
      "independent sets",
      "chordal graphs",
      "hadwigers conjecture implies",
      "hadwigers conjecture states"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2421B"
    }
  }
}