{
  "id": "1607.03959",
  "version": "v1",
  "published": "2016-07-13T23:36:55.000Z",
  "updated": "2016-07-13T23:36:55.000Z",
  "title": "Grünbaum coloring and its generalization to arbitrary dimension",
  "authors": [
    "S. Lawrencenko",
    "M. N. Vyalyi",
    "L. V. Zgonnik"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO",
    "cs.CC",
    "math.GT",
    "math.HO"
  ],
  "abstract": "This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Gr\\\"unbaum colorings, their existence and usage. In particular, one of the most striking significances of Gr\\\"unbaum's Conjecture in the 2-dimensional case is its equivalence to the 4-Color Theorem. The notion of Gr\\\"unbaum coloring is extended from the 2-dimensional case to the case of arbitrary finite hyper-dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-13T23:36:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05B05",
      "52C20",
      "52C22",
      "05B07",
      "57M20",
      "57M15"
    ],
    "keywords": [
      "arbitrary dimension",
      "grünbaum coloring",
      "generalization",
      "arbitrary finite hyper-dimensions",
      "current research"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}