{
  "id": "cond-mat/0409448",
  "version": "v2",
  "published": "2004-09-17T09:32:37.000Z",
  "updated": "2004-11-01T10:09:57.000Z",
  "title": "How many colors to color a random graph? Cavity, Complexity, Stability and all that",
  "authors": [
    "Florent Krzakala"
  ],
  "comment": "4 pages, 2 figures, proceeding of \"Statistical Physics of Disordered Systems and Its Applications\", Hayama (Japan), July 2004",
  "journal": "Progress of Theoretical Physics Supplement No.157 (2005) pp. 357-360",
  "doi": "10.1143/PTPS.157.357",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We review recent progress on the statiscal physics study of the problem of coloring random graphs with q colors. We discuss the existence of a threeshold at connectivity c_q=2q log q-log q-1+o(1) separting two phases which are respectivily COL(orable) and UNCOL(orable) with q colors; We also argue that the so-called one-step replica symmetry breaking ansatz used to derive these results give it exact threshold values, and draw a general phase diagram of the problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-01T10:09:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graph",
      "one-step replica symmetry breaking ansatz",
      "complexity",
      "statiscal physics study",
      "exact threshold values"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}