{
  "id": "2208.06358",
  "version": "v1",
  "published": "2022-08-12T16:31:40.000Z",
  "updated": "2022-08-12T16:31:40.000Z",
  "title": "Subdivisions with congruence constraints in digraphs of large chromatic number",
  "authors": [
    "Raphael Steiner"
  ],
  "comment": "5 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for every digraph $F$ and every assignment of pairs of integers $(r_e,q_e)_{e \\in A(F)}$ to its arcs there exists an integer $N$ such that every digraph $D$ with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of length congruent to $r_e$ modulo $q_e$, for every $e \\in A(F)$. This generalizes to the directed setting the analogous result by Thomassen for undirected graphs, and at the same time yields a novel short proof of his result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-12T16:31:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C20",
      "05C38",
      "05C10",
      "05C83"
    ],
    "keywords": [
      "large chromatic number",
      "congruence constraints",
      "subdivision",
      "novel short proof",
      "dichromatic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}