{
  "id": "1110.4205",
  "version": "v1",
  "published": "2011-10-19T08:30:27.000Z",
  "updated": "2011-10-19T08:30:27.000Z",
  "title": "A Tur'an-type problem for circular arc graphs",
  "authors": [
    "Rosalie Carlson",
    "Stephen Flood",
    "Kevin O'Neill",
    "Francis Edward Su"
  ],
  "comment": "18 pages, 8 figures, related papers at http://www.math.hmc.edu/~su/papers.html",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A circular arc graph is the intersection graph of a collection of connected arcs on the circle. We solve a Tur'an-type problem for circular arc graphs: for n arcs, if m and M are the minimum and maximum number of arcs that contain a common point, what is the maximum number of edges the circular arc graph can contain? We establish a sharp bound and produce a maximal construction. For a fixed m, this can be used to show that if the circular arc graph has enough edges, there must be a point that is covered by at least M arcs. In the case m=0, we recover results for interval graphs established by Abbott and Katchalski (1979). We suggest applications to voting situations with interval or circular political spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-19T08:30:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "91B12"
    ],
    "keywords": [
      "circular arc graph",
      "turan-type problem",
      "maximum number",
      "intersection graph",
      "interval graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.4205C"
    }
  }
}