Another proof of Seymour's 6-flow theorem

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-04-25 DOI:10.1002/jgt.23091

Matt DeVos, Jessica McDonald, Kathryn Nurse

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引用次数: 0

Abstract

In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group $Z_{2} \times Z_{3}$ (in fact, he offers two proofs of this result). In this note, we give a new short proof of a generalization of this theorem where $Z_{2} \times Z_{3}$ -valued functions are found subject to certain boundary constraints.

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西摩 6 流定理的另一个证明

1981 年，西摩证明了他著名的 6 流定理，断言每个 2 边连接的图在群中都有一个无处为零的流（事实上，他对这一结果提供了两个证明）。在本注释中，我们给出了这一定理广义化的一个新的简短证明，在此定理中，-值函数是在某些边界约束条件下找到的。

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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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .