{
  "id": "1503.00438",
  "version": "v1",
  "published": "2015-03-02T08:36:59.000Z",
  "updated": "2015-03-02T08:36:59.000Z",
  "title": "An improved bound on the sizes of matchings guaranteeing a rainbow matching",
  "authors": [
    "Dennis Clemens",
    "Julia Ehrenmüller"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A conjecture by Aharoni and Berger states that every family of $n$ matchings of size $n+1$ in a bipartite multigraph contains a rainbow matching of size $n$. In this paper we prove that matching sizes of $(3/2 + o(1)) n$ suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best known one in case we only aim to find a rainbow matching of size $n-1$. This improves previous results by Aharoni, Charbit and Howard, and Kotlar and Ziv.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-02T08:36:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rainbow matching",
      "matchings guaranteeing",
      "bipartite multigraph contains",
      "berger states",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}