{
  "id": "2409.09758",
  "version": "v1",
  "published": "2024-09-15T14:58:46.000Z",
  "updated": "2024-09-15T14:58:46.000Z",
  "title": "Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof",
  "authors": [
    "Paul Seymour"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G be an acyclic digraph, and let a, b, c, d be vertices, where a, b are sources, c, d are sinks, and every other vertex has in-degree and out-degree at least two. In 1985, Thomassen showed that there do not exist disjoint directed paths from a to c and from b to d, if and only if G can be drawn in a closed disc with a, b, c, d drawn in the boundary in order. We give a shorter proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-15T14:58:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10"
    ],
    "keywords": [
      "shorter proof",
      "acyclic digraph",
      "thomassens theorem",
      "two-linkage problem",
      "disjoint directed paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}