{
  "id": "1511.02427",
  "version": "v1",
  "published": "2015-11-08T02:25:31.000Z",
  "updated": "2015-11-08T02:25:31.000Z",
  "title": "On the chromatic number of structured Cayley graphs",
  "authors": [
    "Mohammad Bardestani",
    "Keivan Mallahi-Karai"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1507.05300",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "In this note, we will study the chromatic number of Cayley graphs of algebraic groups that arise from algebraic constructions. Using Lang-Weil bound and Gowers' mixing inequality for quasirandom groups, we will establish lower bounds on the chromatic number of these graphs. This provides a lower bound for the chromatic number of Cayley graphs of the regular graphs associated to the ring of $n\\times n$ matrices over finite fields. Using Weil's bound for Kloosterman sums we will also prove an analogous result for $\\mathrm{SL}_2$ over finite rings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-08T02:25:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic number",
      "structured cayley graphs",
      "algebraic groups",
      "finite fields",
      "algebraic constructions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}