{
  "id": "2004.12561",
  "version": "v1",
  "published": "2020-04-27T03:03:03.000Z",
  "updated": "2020-04-27T03:03:03.000Z",
  "title": "A better bound on the size of rainbow matchings",
  "authors": [
    "Hongliang Lu",
    "Yan Wang",
    "Xingxing Yu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Aharoni and Howard conjectured that, for positive integers $n,k,t$ with $n\\ge k$ and $n\\ge t$, if $F_1,\\ldots, F_t\\subseteq {[n]\\choose k}$ such that $|F_i|>{n\\choose k}-{n-t+1\\choose k}$ for $i\\in [t]$ then there exist $e_i\\in F_i$ for $i\\in [t]$ such that $e_1,\\ldots,e_t$ are pairwise disjoint. Huang, Loh, and Sudakov proved this conjecture for $t<n/(3k^2)$. In this paper, we show that this conjecture holds for $t\\le n/(2k)$ and $n$ sufficiently large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-27T03:03:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rainbow matchings",
      "better bound",
      "conjecture holds",
      "positive integers",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}