{
  "id": "1012.3847",
  "version": "v3",
  "published": "2010-12-17T10:56:33.000Z",
  "updated": "2011-06-07T18:05:15.000Z",
  "title": "Chromatic polynomials of complementary (n,k)-clique pairs",
  "authors": [
    "Adam Bohn"
  ],
  "comment": "Replaced by a longer version, containing this note as a subsection",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the complement of that of the other. We prove a precise relation between the chromatic polynomials of the graphs in such a pair, showing that they have the same splitting field, and that the number of acyclic orientations of each graph is determined by the number of proper vertex-colourings of the other.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-07T18:05:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic polynomials",
      "complementary",
      "arbitrary number",
      "precise relation",
      "acyclic orientations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.3847B"
    }
  }
}