{
  "id": "1108.4140",
  "version": "v3",
  "published": "2011-08-20T19:11:31.000Z",
  "updated": "2012-12-10T22:19:39.000Z",
  "title": "Tiling 3-uniform hypergraphs with K_4^3-2e",
  "authors": [
    "Andrzej Czygrinow",
    "Louis DeBiasio",
    "Brendan Nagle"
  ],
  "comment": "10 pages, 1 figure, to appear in \"Journal of Graph Theory\"",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let K_4^3-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n, K_4^3-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree \\delta_2(G) \\geq d contains \\floor{n/4} vertex-disjoint copies of K_4^3-2e. K\\\"uhn and Osthus proved that t(n, K_4^3-2e) = (1 + o(1))n/4 holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, t(n, K_4^3-2e) = n/4 when n/4 is odd, and t(n, K_4^3-2e) = n/4+1 when n/4 is even. A main ingredient in our proof is the recent `absorption technique' of R\\\"odl, Ruci\\'nski and Szemer\\'edi.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-10T22:19:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C65",
      "05C70"
    ],
    "keywords": [
      "hypergraph",
      "minimum pair-degree",
      "vertex-disjoint copies",
      "smallest integer",
      "exact counterpart"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4140C"
    }
  }
}