{
  "id": "1111.1558",
  "version": "v1",
  "published": "2011-11-07T12:27:57.000Z",
  "updated": "2011-11-07T12:27:57.000Z",
  "title": "On proper colorings of hypergraphs",
  "authors": [
    "Nick Gravin",
    "Dmitrii Karpov"
  ],
  "comment": "10 pages, 3 figure",
  "journal": "Journal of Mathematical Sciences, Volume 184, Issue 5 (2012), pp. 595-600",
  "doi": "10.1007/s10958-012-0884-2",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{H}$ be a hypergraph of maximal vertex degree $\\Delta$, such that each its hyperedge contains at least $\\delta$ vertices. Let $k=\\lceil\\frac{2\\Delta}{\\delta}\\rceil$. We prove that (i) The hypergraph $\\mathcal{H}$ admits proper vertex coloring in $k+1$ colors. (ii) The hypergraph $\\mathcal{H}$ admits proper vertex coloring in $k$ colors, if $\\delta\\ge 3$ and $k\\ge 3$. As a consequence of these results we derive upper bounds on the number of colors in dynamic colorings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-07T12:27:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "proper colorings",
      "hypergraph",
      "admits proper vertex coloring",
      "maximal vertex degree",
      "dynamic colorings"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1558G"
    }
  }
}