{
  "id": "2006.08941",
  "version": "v1",
  "published": "2020-06-16T06:15:34.000Z",
  "updated": "2020-06-16T06:15:34.000Z",
  "title": "Confining the Robber on Cographs",
  "authors": [
    "Masood Masjoody"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "In this paper the notions of {\\em trapping} and {\\em confining} the robber on a graph are introduced. We present some necessary conditions for graphs $G$ not containing the path on $k$ vertices (for some $k\\ge 4$) as an induced subgraph so that $k-3$ cops do not have a winning strategy on $G$. Utilizing the latter conditions together with a characterization of cographs, we show that on cograph the robber can always be confined by one cop. We conclude by posing a conjecture about the confining cop number of $P_k$-free graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T06:15:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C57",
      "91A46"
    ],
    "keywords": [
      "necessary conditions",
      "confining cop number",
      "free graphs",
      "induced subgraph",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}