{
  "id": "0806.0178",
  "version": "v2",
  "published": "2008-06-02T14:37:52.000Z",
  "updated": "2017-10-18T11:55:00.000Z",
  "title": "On the concentration of the chromatic number of random graphs",
  "authors": [
    "Alex Scott"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let 0<p<1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic number of a random graph in G(n,p) is concentrated in an interval of length about n^{1/2}. In this explanatory note, we give a proof of a result due due Noga Alon, showing that the chromatic number is concentrated in an interval of length about n^{1/2}/log n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-02T14:37:52.000Z",
      "abstract": "Let 0<p<1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic number of a random graph in G(n,p) is concentrated in an interval of length about n^{1/2}. We give an improvement on this, showing that the chromatic number is concentrated in an interval of length about n^{1/2}/\\log n.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Alexander Scott"
      ]
    },
    {
      "version": "v2",
      "updated": "2017-10-18T11:55:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C80"
    ],
    "keywords": [
      "chromatic number",
      "random graph",
      "concentration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.0178S"
    }
  }
}