{
  "id": "2006.02998",
  "version": "v1",
  "published": "2020-06-04T16:37:00.000Z",
  "updated": "2020-06-04T16:37:00.000Z",
  "title": "4-cop-win graphs have at least 19 vertices",
  "authors": [
    "Jérémie Turcotte",
    "Samuel Yvon"
  ],
  "comment": "27 pages, 9 figures. Data and code available at https://www.jeremieturcotte.com/research/min4cops/ . We are open to comments and are happy to help anyone understand the code",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We show that the cop number of any graph on 18 or fewer vertices is at most 3. This answers a specific case of a question posed by Baird et al. on the minimum order of 4-cop-win graphs, first appearing in 2011. We also find all 3-cop-win graphs on 11 vertices, narrow down the possible 4-cop-win graphs on 19 vertices and get some progress on finding the minimum order of 3-cop-win planar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-04T16:37:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C57",
      "05C35",
      "05C85",
      "90C35",
      "68V05"
    ],
    "keywords": [
      "minimum order",
      "planar graphs",
      "cop number",
      "fewer vertices",
      "specific case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}