{
  "id": "1404.1136",
  "version": "v3",
  "published": "2014-04-04T02:49:01.000Z",
  "updated": "2014-08-06T14:46:47.000Z",
  "title": "Near Perfect Matchings in $k$-uniform Hypergraphs",
  "authors": [
    "Jie Han"
  ],
  "comment": "8 pages, 0 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $H$ be a $k$-uniform hypergraph on $n$ vertices where $n$ is a sufficiently large integer not divisible by $k$. We prove that if the minimum $(k-1)$-degree of $H$ is at least $\\lfloor n/k \\rfloor$, then $H$ contains a matching with $\\lfloor n/k\\rfloor$ edges. This confirms a conjecture of R\\\"odl, Ruci\\'nski and Szemer\\'edi, who proved that the minimum $(k-1)$-degree $n/k+O(\\log n)$ suffices. More generally, we show that $H$ contains a matching of size $d$ if its minimum codegree is $d<n/k$, which is also best possible.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-06T14:46:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform hypergraph",
      "perfect matchings",
      "sufficiently large integer",
      "minimum codegree",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1136H"
    }
  }
}