{
  "id": "1704.00487",
  "version": "v1",
  "published": "2017-04-03T09:17:47.000Z",
  "updated": "2017-04-03T09:17:47.000Z",
  "title": "On the independence number of graphs related to a polarity",
  "authors": [
    "Sam Mattheus",
    "Francesco Pavese",
    "Leo Storme"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate the independence number of two graphs constructed from a polarity of $\\mathrm{PG}(2,q)$. For the first graph under consideration, the Erd\\H{o}s-R\\'enyi graph $ER_q$, we provide an improvement on the known lower bounds on its independence number. In the second part of the paper we consider the Erd\\H{o}s-R\\'enyi hypergraph of triangles $\\mathcal{H}_q$. We determine the exact magnitude of the independence number of $\\mathcal{H}_q$, $q$ even. This solves a problem posed by Mubayi and Williford.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-03T09:17:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05B25",
      "05C69",
      "05C35"
    ],
    "keywords": [
      "independence number",
      "first graph",
      "lower bounds",
      "second part",
      "exact magnitude"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}