Every 2-connected {claw, Z2}-free graph with minimum degree at least 4 contains two CISTs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-09-03 DOI:10.1016/j.dam.2024.08.020

Xiaodong Chen , Jiayuan Zhang , Liming Xiong , Guifu Su

引用次数: 0

Abstract

If a graph $G$ contains two spanning trees $T_{1}, T_{2}$ such that for each two distinct vertices $x, y$ of $G,$ the $(x, y)$ -path in each $T_{i}$ has no common edge and no common vertex except for the two ends, then $T_{1}, T_{2}$ are called two completely independent spanning trees (CISTs) of $G, i \in {1, 2} .$ There are several results on the existence of two CISTs. In this paper, we prove that every 2-connected {claw, $Z_{2}$ }-free graph with minimum degree at least 4 contains two CISTs. The bound of the minimum degree in our result is best possible.

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最小阶数至少为 4 的每个 2 连接{claw, Z2} 无图都包含两个 CIST

如果一个图 G 包含两棵生成树 T1,T2，对于 G 的两个不同顶点 x,y，每个 Ti 中的（x,y）路径除了两端外没有公共边和公共顶点，那么 T1,T2 被称为 G 的两棵完全独立生成树（CIST），i∈{1,2}。关于两棵完全独立生成树的存在性有多种结果。在本文中，我们证明了每一个最小度至少为 4 的 2 连接{claw, Z2} 无图都包含两个 CIST。在我们的结果中，最小度的约束是最好的。

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 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.