托马森关于非循环图中双链路问题的定理：简明证明

arXiv - MATH - Combinatorics Pub Date : 2024-09-15 DOI:arxiv-2409.09758

Paul Seymour

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引用次数: 0

摘要

设 G 是一个非循环数图，设 a、b、c、d 为顶点，其中 a、b 为源顶点，c、d 为汇顶顶点，每个其他顶点的入度和出度至少为 2。1985 年，托马森（Thomassen）证明了当且仅当 G 可以画成一个封闭的圆盘，并在边界上依次画出 a、b、c、d 时，不存在从 a 到 c 和从 b 到 d 的互不相交的有向路径。我们给出一个更简短的证明。

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

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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arXiv - MATH - Combinatorics

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