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arXiv · 2409.09758

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

Paul Seymour
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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.

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Paul Seymour. 2024-09-15. Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof. https://arxiv.org/abs/2409.09758

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