Sparse graphs with an independent or foresty minimum vertex cut

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-30 DOI:10.1016/j.disc.2025.114658

Kun Cheng, Yurui Tang, Xingzhi Zhan

引用次数: 0

Abstract

A connected graph is called fragile if it contains an independent vertex cut. In 2002 Chen and Yu proved that every connected graph of order n and size at most

2 n - 4

is fragile, and in 2013 Le and Pfender characterized the non-fragile graphs of order n and size

2 n - 3

. It is natural to consider minimum vertex cuts. We prove two results. (1) Every connected graph of order n with

n \geq 7

and size at most

⌊ 3 n / 2 ⌋

has an independent minimum vertex cut; (2) every connected graph of order n with

n \geq 7

and size at most 2n has a foresty minimum vertex cut. Both results are best possible.

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具有独立或森林最小顶点切割的稀疏图

如果连通图包含独立的顶点切割，则称为脆弱图。2002年Chen和Yu证明了最大2n−4的n阶连通图都是脆弱的，2013年Le和Pfender刻画了最大2n−3的n阶非脆弱图。考虑最小顶点切割是很自然的。我们证明了两个结果。(1)每一个n阶连通图，且n≥7且最大为⌊3n/2⌋，都有一个独立的最小顶点切割；(2)每一个n≥7且最大为2n的n阶连通图都有一个森林最小顶点切割。两种结果都是最好的。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.