{
  "id": "2008.13224",
  "version": "v1",
  "published": "2020-08-30T17:31:45.000Z",
  "updated": "2020-08-30T17:31:45.000Z",
  "title": "Oriented cycles in digraphs of large outdegree",
  "authors": [
    "Lior Gishboliner",
    "Raphael Steiner",
    "Tibor Szabó"
  ],
  "comment": "28 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1985, Mader conjectured that for every acyclic digraph $F$ there exists $K=K(F)$ such that every digraph $D$ with minimum out-degree at least $K$ contains a subdivision of $F$. This conjecture remains widely open, even for digraphs $F$ on five vertices. Recently, Aboulker, Cohen, Havet, Lochet, Moura and Thomass\\'{e} studied special cases of Mader's problem and made the following conjecture: for every $\\ell \\geq 2$ there exists $K = K(\\ell)$ such that every digraph $D$ with minimum out-degree at least $K$ contains a subdivision of every orientation of a cycle of length $\\ell$. We prove this conjecture and answer further open questions raised by Aboulker et al.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-30T17:31:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C07",
      "05C20",
      "05C83"
    ],
    "keywords": [
      "large outdegree",
      "oriented cycles",
      "minimum out-degree",
      "acyclic digraph",
      "open questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}