{
  "id": "2301.13175",
  "version": "v1",
  "published": "2023-01-30T18:42:34.000Z",
  "updated": "2023-01-30T18:42:34.000Z",
  "title": "Cops and robbers on $P_5$-free graphs",
  "authors": [
    "Maria Chudnovsky",
    "Sergey Norin",
    "Paul Seymour",
    "Jérémie Turcotte"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We prove that every connected $P_5$-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected $P_5$-free graph $G$ with independence number at least three contains a three-vertex induced path with vertices $a \\hbox{-} b \\hbox{-} c$ in order, such that every neighbour of $c$ is also adjacent to one of $a,b$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-30T18:42:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C57"
    ],
    "keywords": [
      "free graph",
      "cop number",
      "independence number",
      "three-vertex induced path",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}