Linkages and removable paths avoiding vertices

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-15 DOI:10.1016/j.jctb.2024.06.006

Xiying Du, Yanjia Li, Shijie Xie , Xingxing Yu

引用次数: 0

Abstract

A graph G is $(2, m)$ -linked if, for any distinct vertices $a_{1}, \dots, a_{m}, b_{1}, b_{2}$ in G, there exist disjoint connected subgraphs $A, B$ of G such that $a_{1}, \dots, a_{m} \in V (A)$ and $b_{1}, b_{2} \in V (B)$ . A fundamental result in structural graph theory is the characterization of $(2, 2)$ -linked graphs. It appears to be difficult to characterize $(2, m)$ -linked graphs for $m \geq 3$ . In this paper, we provide a partial characterization of $(2, m)$ -linked graphs. This implies that every $(2 m + 2)$ -connected graphs G is $(2, m)$ -linked and for any distinct vertices $a_{1}, \dots, a_{m}, b_{1}, b_{2}$ of G, there is a path P in G between $b_{1}$ and $b_{2}$ and avoiding ${a_{1}, \dots, a_{m}}$ such that $G - P$ is connected, improving a previous connectivity bound of 10m.

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避开顶点的连线和可移动路径

如果对于 G 中任何不同的顶点 a1,...,am,b1,b2，存在 G 的互不相交的连通子图 A,B，使得 a1,...,am∈V(A)和 b1,b2∈V(B)，则图 G 是 (2,m)-linked 的。结构图理论的一个基本结果是（2,2）连接图的特征描述。要描述 m≥3 的 (2,m) 链接图似乎很难。本文提供了 (2,m) 链接图的部分特征。这意味着每个 (2m+2)-linkected graphs G 都是 (2,m)-linked 的，并且对于 G 的任何不同顶点 a1,...,am,b1,b2，G 中都存在一条路径 P，该路径 P 位于 b1 和 b2 之间，并避开 {a1,...,am}，这样 G-P 就是连通的，从而改善了之前 10m 的连通性约束。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.