{
  "id": "1107.5544",
  "version": "v2",
  "published": "2011-07-27T17:24:42.000Z",
  "updated": "2011-09-15T00:18:00.000Z",
  "title": "The size of a hypergraph and its matching number",
  "authors": [
    "Hao Huang",
    "Po-Shen Loh",
    "Benny Sudakov"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "More than forty years ago, Erd\\H{o}s conjectured that for any T <= N/K, every K-uniform hypergraph on N vertices without T disjoint edges has at most max{\\binom{KT-1}{K}, \\binom{N}{K} - \\binom{N-T+1}{K}} edges. Although this appears to be a basic instance of the hypergraph Tur\\'an problem (with a T-edge matching as the excluded hypergraph), progress on this question has remained elusive. In this paper, we verify this conjecture for all T < N/(3K^2). This improves upon the best previously known range T = O(N/K^3), which dates back to the 1970's.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-15T00:18:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D15",
      "05D05",
      "05C35",
      "05C70",
      "05C65"
    ],
    "keywords": [
      "matching number",
      "hypergraph turan problem",
      "basic instance",
      "k-uniform hypergraph",
      "disjoint edges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5544H"
    }
  }
}