The immersion-minimal infinitely edge-connected graph

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2023-11-08 DOI:10.1016/j.jctb.2023.10.007

Paul Knappe , Jan Kurkofka

引用次数: 0

Abstract

We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an immersion minor.

By contrast, any minimal list of infinitely edge-connected graphs represented in all such graphs as topological minors must be uncountable.

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浸入极小无限边连通图

我们证明了存在一个唯一的浸入最小无限边连通图:每一个这样的图都包含了一半的Farey图，它本身是无限边连通的，作为浸入小图。相反，在所有这样的图中表示为拓扑子图的无限边连通图的最小列表必须是不可数的。

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 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.