{
  "id": "math/0311449",
  "version": "v1",
  "published": "2003-11-25T16:44:23.000Z",
  "updated": "2003-11-25T16:44:23.000Z",
  "title": "Asymptotically optimal $K_k$-packings of dense graphs via fractional $K_k$-decompositions",
  "authors": [
    "Raphael Yuster"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $H$ be a fixed graph. A {\\em fractional $H$-decomposition} of a graph $G$ is an assignment of nonnegative real weights to the copies of $H$ in $G$ such that for each $e \\in E(G)$, the sum of the weights of copies of $H$ containing $e$ in precisely one. An {\\em $H$-packing} of a graph $G$ is a set of edge disjoint copies of $H$ in $G$. The following results are proved. For every fixed $k > 2$, every graph with $n$ vertices and minimum degree at least $n(1-1/9k^{10})+o(n)$ has a fractional $K_k$-decomposition and has a $K_k$-packing which covers all but $o(n^2)$ edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-25T16:44:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C35",
      "05D40"
    ],
    "keywords": [
      "dense graphs",
      "asymptotically optimal",
      "fractional",
      "decomposition",
      "edge disjoint copies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11449Y"
    }
  }
}