English

Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof

Combinatorics 2024-09-17 v1

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.

Cite

@article{arxiv.2409.09758,
  title  = {Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof},
  author = {Paul Seymour},
  journal= {arXiv preprint arXiv:2409.09758},
  year   = {2024}
}
R2 v1 2026-06-28T18:45:14.163Z