{
  "id": "1110.3490",
  "version": "v2",
  "published": "2011-10-16T14:50:44.000Z",
  "updated": "2013-03-08T15:35:43.000Z",
  "title": "On perfect packings in dense graphs",
  "authors": [
    "József Balogh",
    "Alexandr V. Kostochka",
    "Andrew Treglown"
  ],
  "comment": "18 pages, 1 figure. Electronic Journal of Combinatorics 20(1) (2013) #P57. This version contains an open problem section",
  "categories": [
    "math.CO"
  ],
  "abstract": "We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect H-packings: Given positive integers n, r, D, we characterise the edge density threshold that ensures a perfect K_r-packing in any graph G on n vertices and with minimum degree at least D. We also give two conjectures concerning degree sequence conditions which force a graph to contain a perfect H-packing. Other related embedding problems are also considered. Indeed, we give a structural result concerning K_r-free graphs that satisfy a certain degree sequence condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-08T15:35:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C35",
      "05C70"
    ],
    "keywords": [
      "dense graphs",
      "perfect packings",
      "conjectures concerning degree sequence conditions",
      "problems concerning perfect h-packings",
      "edge density threshold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3490B"
    }
  }
}