{
  "id": "1007.0710",
  "version": "v1",
  "published": "2010-07-05T16:07:51.000Z",
  "updated": "2010-07-05T16:07:51.000Z",
  "title": "Vertex colorings of simplicial complexes",
  "authors": [
    "Natalia Dobrinskaya",
    "Jesper M. Møller",
    "Dietrich Notbohm"
  ],
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "We define an (r,s)-coloring of an abstract simplicial complex to be a coloring using r colors of the vertices so that in any simplex at most s vertices have the same color. We translate the problem of finding an (r,s)-coloring of a given simplex to a topological problem and to a ring theoretic problem. The topological version involves vector bundles over Davis--Januszkiewicz spaces and the algebraic one involves factorizations in Stanley-Reisner rings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-05T16:07:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "55R25"
    ],
    "keywords": [
      "simplicial complexes",
      "vertex colorings",
      "abstract simplicial complex",
      "stanley-reisner rings",
      "davis-januszkiewicz spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0710D"
    }
  }
}