{
  "id": "2101.04590",
  "version": "v1",
  "published": "2021-01-12T16:42:12.000Z",
  "updated": "2021-01-12T16:42:12.000Z",
  "title": "Complete minors in digraphs with given dichromatic number",
  "authors": [
    "Tamás Mészáros",
    "Raphael Steiner"
  ],
  "comment": "7 pages, note",
  "categories": [
    "math.CO"
  ],
  "abstract": "The dichromatic number $\\vec{\\chi}(D)$ of a digraph $D$ is the smallest $k$ for which it admits a $k$-coloring where every color class induces an acyclic subgraph. Inspired by Hadwiger's conjecture for undirected graphs, several groups of authors have recently studied the containment of directed graph minors in digraphs with given dichromatic number. In this short note we improve several of the existing bounds and prove almost linear bounds by reducing the problem to a recent result of Postle on Hadwiger's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-12T16:42:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C20",
      "05C83"
    ],
    "keywords": [
      "dichromatic number",
      "complete minors",
      "hadwigers conjecture",
      "color class induces",
      "linear bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}