无2团切集的最小连通图的刻画

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-09-08 DOI:10.1016/j.dam.2025.08.059

Hengzhe Li, Qiong Wang

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引用次数: 0

摘要

团切集是研究图分解和图表征的重要工具。对于整数k≥1，连通图的k-团切集是一个k-团，它的移除使图断开。无1团切集的最小连通图族就是Dirac在1967年描述的最小2连通图族。狄拉克还证明了每一个最小2连通图都没有三角形。本文刻画了没有2团切集的最小连通图族，并证明了每个没有2团切集的最小连通图也没有三角形。

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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A characterization of minimally connected graphs without 2-clique cutsets

Clique cutsets are an important tool for studying both graph decomposition and graph characterization. For an integer

k \geq 1

, a

k

-clique cutset of a connected graph is a

k

-clique whose removal disconnects the graph. The family of minimally connected graphs without 1-clique cutsets is just the family of minimally 2-connected graphs, which was characterized by Dirac in 1967. Dirac also proved that each minimally 2-connected graph has no triangles. In this paper, we characterize the family of minimally connected graphs without 2-clique cutsets, and show that each minimally connected graph without 2-clique cutsets also has no triangles.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.