{
  "id": "1009.1298",
  "version": "v2",
  "published": "2010-09-07T14:08:10.000Z",
  "updated": "2012-11-13T17:17:29.000Z",
  "title": "Matchings in 3-uniform hypergraphs",
  "authors": [
    "Daniela Kühn",
    "Deryk Osthus",
    "Andrew Treglown"
  ],
  "comment": "18 pages, 1 figure. To appear in JCTB",
  "categories": [
    "math.CO"
  ],
  "abstract": "We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose that H is a sufficiently large 3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than \\binom{n-1}{2}-\\binom{2n/3}{2}, then H contains a perfect matching. This bound is tight and answers a question of Han, Person and Schacht. More generally, we show that H contains a matching of size d\\le n/3 if its minimum vertex degree is greater than \\binom{n-1}{2}-\\binom{n-d}{2}, which is also best possible. This extends a result of Bollobas, Daykin and Erdos.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-13T17:17:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C65",
      "05C70"
    ],
    "keywords": [
      "minimum vertex degree",
      "hypergraph",
      "perfect matching",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1298K"
    }
  }
}