{
  "id": "2007.13111",
  "version": "v1",
  "published": "2020-07-26T12:07:35.000Z",
  "updated": "2020-07-26T12:07:35.000Z",
  "title": "The Oriented Chromatic Number of the Hexagonal Grid is 6",
  "authors": [
    "Antoni Lozano"
  ],
  "comment": "8 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The oriented chromatic number of a directed graph $G$ is the minimum order of an oriented graph to which $G$ has a homomorphism. The oriented chromatic number $\\chi_o({\\cal F})$ of a graph family ${\\cal F}$ is the maximum oriented chromatic number over any orientation of any graph in ${\\cal F}$. For the family of hexagonal grids ${\\cal H}_2$, Bielak (2006) proved that $5 \\le \\chi_o({\\cal H}_2) \\le 6$. Here we close the gap by showing that $\\chi_o({\\cal H}_2) \\ge 6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-26T12:07:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C85"
    ],
    "keywords": [
      "hexagonal grid",
      "maximum oriented chromatic number",
      "minimum order",
      "oriented graph",
      "homomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}