{
  "id": "1002.4210",
  "version": "v3",
  "published": "2010-02-22T22:08:20.000Z",
  "updated": "2012-06-10T08:13:04.000Z",
  "title": "Unique-maximum and conflict-free colorings for hypergraphs and tree graphs",
  "authors": [
    "Panagiotis Cheilaris",
    "Balázs Keszegh",
    "Dömötör Pálvölgyi"
  ],
  "comment": "added some references and expanded some proofs",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color appears only once. In a conflict-free coloring, in every hyperedge of the hypergraph there is a color that appears only once. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-10T08:13:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tree graphs",
      "conflict-free coloring",
      "maximum color appears",
      "conflict-free chromatic numbers",
      "relationship"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4210C"
    }
  }
}