{
  "id": "math/0605189",
  "version": "v1",
  "published": "2006-05-08T08:22:52.000Z",
  "updated": "2006-05-08T08:22:52.000Z",
  "title": "Perfect packings with complete graphs minus an edge",
  "authors": [
    "Oliver Cooley",
    "Daniela Kühn",
    "Deryk Osthus"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let K_r^- denote the graph obtained from K_r by deleting one edge. We show that for every integer r\\ge 4 there exists an integer n_0=n_0(r) such that every graph G whose order n\\ge n_0 is divisible by r and whose minimum degree is at least (1-1/chi_{cr}(K_r^-))n contains a perfect K_r^- packing, i.e. a collection of disjoint copies of K_r^- which covers all vertices of G. Here chi_{cr}(K_r^-)=r(r-2)/(r-1) is the critical chromatic number of K_r^-. The bound on the minimum degree is best possible and confirms a conjecture of Kawarabayashi for large n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-08T08:22:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C15"
    ],
    "keywords": [
      "complete graphs minus",
      "perfect packings",
      "minimum degree",
      "disjoint copies",
      "critical chromatic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5189C"
    }
  }
}