{
  "id": "1903.11484",
  "version": "v1",
  "published": "2019-03-27T15:23:25.000Z",
  "updated": "2019-03-27T15:23:25.000Z",
  "title": "Cop number of $2K_2$-free graphs",
  "authors": [
    "Vaidy Sivaraman",
    "Stephen Testa"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We prove that the cop number of a $2K_2$-free graph is at most $2$ if it has diameter $3$ or does not have an induced cycle of length $k$, where $k \\ \\in \\{3,4,5\\}$. We conjecture that the cop number of every $2K_2$-free graph is at most $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-27T15:23:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graph",
      "cop number",
      "induced cycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}