{
  "id": "1812.06230",
  "version": "v1",
  "published": "2018-12-15T03:43:29.000Z",
  "updated": "2018-12-15T03:43:29.000Z",
  "title": "Cops and Robbers on Graphs with a Set of Forbidden Induced Subgraphs",
  "authors": [
    "Masood Masjoody",
    "Ladislav Stacho"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "It is known that the class of all graphs not containing a graph $H$ as an induced subgraph is cop-bounded if and only if $H$ is a forest whose every component is a path. In this study, we characterize all sets $\\mathscr{H}$ of graphs with some $k\\in \\mathbb{N}$ bounding the diameter of members of $\\mathscr{H}$ from above, such that $\\mathscr{H}$-free graphs, i.e. graphs with no member of $\\mathscr{H}$ as an induced subgraph, are cop-bounded. This, in particular, gives a characterization of cop-bounded classes of graphs defined by a finite set of connected graphs as forbidden induced subgraphs. Furthermore, we extend our characterization to the case of cop-bounded classes of graphs defined by a set $\\mathscr{H}$ of forbidden graphs such that there is $k\\in\\mathbb{N}$ bounding the diameter of components of members of $\\mathscr{H}$ from above.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-15T03:43:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C57",
      "91A46"
    ],
    "keywords": [
      "forbidden induced subgraphs",
      "cop-bounded classes",
      "forbidden graphs",
      "finite set",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}