{
  "id": "1111.5501",
  "version": "v2",
  "published": "2011-11-23T14:25:30.000Z",
  "updated": "2013-09-19T23:22:39.000Z",
  "title": "Conflict-free coloring of graphs",
  "authors": [
    "Roman Glebov",
    "Tibor Szabó",
    "Gábor Tardos"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the conflict-free chromatic number chi_{CF} of graphs from extremal and probabilistic point of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number an n-vertex graph can have. Our construction is randomized. In relation to this we study the evolution of the conflict-free chromatic number of the Erd\\H{o}s-R\\'enyi random graph G(n,p) and give the asymptotics for p=omega(1/n). We also show that for p \\geq 1/2 the conflict-free chromatic number differs from the domination number by at most 3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-19T23:22:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C15",
      "05C80",
      "05D40",
      "05C69"
    ],
    "keywords": [
      "conflict-free coloring",
      "conflict-free chromatic number differs",
      "maximum conflict-free chromatic number",
      "domination number",
      "random graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5501G"
    }
  }
}