{
  "id": "1303.4061",
  "version": "v1",
  "published": "2013-03-17T14:28:29.000Z",
  "updated": "2013-03-17T14:28:29.000Z",
  "title": "An Erdős--Ko--Rado theorem for matchings in the complete graph",
  "authors": [
    "Vikram Kamat",
    "Neeldhara Misra"
  ],
  "comment": "9 pages, 4 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We consider the following higher-order analog of the Erd\\H{o}s--Ko--Rado theorem. For positive integers r and n with r<= n, let M^r_n be the family of all matchings of size r in the complete graph K_{2n}. For any edge e in E(K_{2n}), the family M^r_n(e), which consists of all sets in M^r_n containing e, is called the star centered at e. We prove that if r<n and A is an intersecting family of matchings in M^r_n, then |A|<=|M^r_n(e)|$, where e is an edge in E(K_{2n}). We also prove that equality holds if and only if A is a star. The main technique we use to prove the theorem is an analog of Katona's elegant cycle method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-17T14:28:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "complete graph",
      "erdős-ko-rado theorem",
      "katonas elegant cycle method",
      "higher-order analog",
      "main technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4061K"
    }
  }
}