无环有向图中双连杆问题的Thomassen定理：一个简短的证明

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-09-11 DOI:10.1016/j.jctb.2025.08.006

Paul Seymour

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引用次数: 0

摘要

设G是一个无环有向图，设a，b,c,d∈V(G)，其中a，b为源，c，d为汇，且其他每一个顶点至少有两个入度和出度。1985年，Thomassen证明了不存在从a到c和从b到d的不相交的有向路径，当且仅当G可以画在封闭圆盘上，a,b,c，d依次画在边界上。我们给出一个简短的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 \in V (G)

, 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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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.