3连通拟阵和简单3连通图中的可分离对

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-09-23 DOI:10.1016/j.jctb.2025.09.003

Nick Brettell , Charles Semple , Gerry Toft

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引用次数: 0

摘要

设M是一个3连通的矩阵。如果M\e\f或M/e/f为3连通，则M中的一对{e，f}是可分离的。Williams（2015）证明，如果M至少有13个元件，则M有一个可拆卸的对，M有一个3元电路或共电路，或M是一个尖峰。我们处理M具有3元电路或共电路的情况，以获得具有至少13个单元的矩阵何时具有可拆卸对的特征。因此，我们刻画了当一个|E(G)|≥13的简单3连通图G有一对边{E，f}使得G\ E \f的G/ E /f是简单3连通的。

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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Detachable pairs in 3-connected matroids and simple 3-connected graphs

Let M be a 3-connected matroid. A pair

{e, f}

in M is detachable if

M ﹨ e ﹨ f

M / e / f

is 3-connected. Williams (2015) proved that if M has at least 13 elements, then at least one of the following holds: M has a detachable pair, M has a 3-element circuit or cocircuit, or M is a spike. We address the case where M has a 3-element circuit or cocircuit, to obtain a characterisation of when a matroid with at least 13 elements has a detachable pair. As a consequence, we characterise when a simple 3-connected graph G with

| E (G) | \geq 13

has a pair of edges

{e, f}

such that

G / e / f

G ﹨ e ﹨ f

is simple and 3-connected.

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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.