{
  "id": "0806.2027",
  "version": "v1",
  "published": "2008-06-12T09:32:31.000Z",
  "updated": "2008-06-12T09:32:31.000Z",
  "title": "Triangle packings and 1-factors in oriented graphs",
  "authors": [
    "Peter Keevash",
    "Benny Sudakov"
  ],
  "comment": "22 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "An oriented graph is a directed graph which can be obtained from a simple undirected graph by orienting its edges. In this paper we show that any oriented graph G on n vertices with minimum indegree and outdegree at least (1/2-o(1))n contains a packing of cyclic triangles covering all but at most 3 vertices. This almost answers a question of Cuckler and Yuster and is best possible, since for n = 3 mod 18 there is a tournament with no perfect triangle packing and with all indegrees and outdegrees (n-1)/2 or (n-1)/2 \\pm 1. Under the same hypotheses, we also show that one can embed any prescribed almost 1-factor, i.e. for any sequence n_1,...,n_t with n_1+...+n_t < n-O(1) we can find a vertex-disjoint collection of directed cycles with lengths n_1,...,n_t. In addition, under quite general conditions on the n_i we can remove the O(1) additive error and find a prescribed 1-factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-12T09:32:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C70"
    ],
    "keywords": [
      "oriented graph",
      "triangle packing",
      "quite general conditions",
      "perfect triangle",
      "minimum indegree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.2027K"
    }
  }
}