{
  "id": "1808.04954",
  "version": "v1",
  "published": "2018-08-15T03:13:17.000Z",
  "updated": "2018-08-15T03:13:17.000Z",
  "title": "Rainbow matchings in properly-colored hypergraphs",
  "authors": [
    "Hao Huang",
    "Tong Li",
    "Guanghui Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A hypergraph $H$ is properly colored if for every vertex $v\\in V(H)$, all the edges incident to $v$ have distinct colors. In this paper, we show that if $H_{1}$, \\cdots, $H_{s}$ are properly-colored $k$-uniform hypergraphs on $n$ vertices, where $n\\geq3k^{2}s$, and $e(H_{i})>{{n}\\choose {k}}-{{n-s+1}\\choose {k}}$, then there exists a rainbow matching of size $s$, containing one edge from each $H_i$. This generalizes some previous results on the Erd\\H{o}s Matching Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-15T03:13:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rainbow matching",
      "properly-colored hypergraphs",
      "edges incident",
      "distinct colors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}