{
  "id": "1904.10113",
  "version": "v1",
  "published": "2019-04-23T01:11:38.000Z",
  "updated": "2019-04-23T01:11:38.000Z",
  "title": "Cops and robbers on oriented toroidal grids",
  "authors": [
    "Sebastian Gonzalez Hermosillo de la Maza",
    "Seyyed Aliasghar Hosseini",
    "Fiachra Knox",
    "Bojan Mohar",
    "Bruce Reed"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Klein bottle and we prove that their cop number is bounded by a constant. We also show that the cop number of every k-regularly oriented toroidal grid is at most 13.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-23T01:11:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cop number",
      "well-known game",
      "straight-ahead orientations",
      "klein bottle",
      "k-regularly oriented toroidal grid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}