{
  "id": "1110.1756",
  "version": "v1",
  "published": "2011-10-08T18:28:03.000Z",
  "updated": "2011-10-08T18:28:03.000Z",
  "title": "About dependence of the number of edges and vertices in hypergraph clique with chromatic number 3",
  "authors": [
    "D. D. Cherkashin",
    "A. B. Kulikov",
    "A. M. Raigorodskii"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1973 P. Erd\\H{o}s and L. Lov\\'asz noticed that any hypergraph whose edges are pairwise intersecting has chromatic number 2 or 3. In the first case, such hypergraph may have any number of edges. However, Erd\\H{o}s and Lov\\'asz proved that in the second case, the number of edges is bounded from above. For example, if a hypergraph is $ n $-uniform, has pairwise intersecting edges, and has chromatic number 3, then the number of its edges does not exceed $ n^n $. Recently D.D. Cherkashin improved this bound (see \\cite{Ch}). In this paper, we further improve it in the case when the number of vertices of an $n$-uniform hypergraph is bounded from above by $ n^m $ with some $ m = m(n) $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-08T18:28:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic number",
      "hypergraph clique",
      "dependence",
      "uniform hypergraph",
      "second case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1756C"
    }
  }
}