{
  "id": "1408.1983",
  "version": "v2",
  "published": "2014-08-08T21:13:31.000Z",
  "updated": "2014-09-23T21:38:15.000Z",
  "title": "Decomposition of bounded degree graphs into $C_4$-free subgraphs",
  "authors": [
    "Ross J. Kang",
    "Guillem Perarnau"
  ],
  "comment": "8 pages; to appear in European Journal of Combinatorics",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that every graph with maximum degree $\\Delta$ admits a partition of its edges into $O(\\sqrt{\\Delta})$ parts (as $\\Delta\\to\\infty$) none of which contains $C_4$ as a subgraph. This bound is sharp up to a constant factor. Our proof uses an iterated random colouring procedure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-08T21:13:31.000Z",
      "comment": "9 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-23T21:38:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05D40",
      "05C35",
      "05C55"
    ],
    "keywords": [
      "bounded degree graphs",
      "free subgraphs",
      "decomposition",
      "constant factor",
      "iterated random colouring procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}