{
  "id": "1811.06160",
  "version": "v1",
  "published": "2018-11-15T03:54:29.000Z",
  "updated": "2018-11-15T03:54:29.000Z",
  "title": "Intersecting Families of Perfect Matchings",
  "authors": [
    "Nathan Lindzey"
  ],
  "comment": "40 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "A family of perfect matchings of $K_{2n}$ is $t$-$intersecting$ if any two members share $t$ or more edges. We prove for any $t \\in \\mathbb{N}$ that every $t$-intersecting family of perfect matchings has size no greater than $(2(n-t) - 1)!!$ for sufficiently large $n$, and that equality holds if and only if the family is composed of all perfect matchings that contain a fixed set of $t$ disjoint edges. This is an asymptotic version of a conjecture of Godsil and Meagher that can be seen as the non-bipartite analogue of the Deza-Frankl conjecture proven by Ellis, Friedgut, and Pilpel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-15T03:54:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect matchings",
      "intersecting family",
      "deza-frankl conjecture proven",
      "equality holds",
      "disjoint edges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}