符号边着色的邻接引理及其在平面图上的应用

IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Li Zhang , Hajo Broersma , You Lu , Shenggui Zhang
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引用次数: 0

摘要

在图的边着色研究中,关键图具有特别重要的意义。一个关于临界图结构的经典结果被称为Vizing邻接引理。这个引理提供了关于临界图中顶点邻域的有用结构信息。Zhang引入了一个处理临界图中一个顶点的第二邻域的邻接引理。这两个邻接引理都是证明沿着色分类结果的有用工具。本文给出了具有偶极大度的临界符号图上的一个邻接引理。这个新的邻接引理可以解释为张氏邻接引理的局部推广。作为新引理的一个应用,我们证明了一个最大度Δ≥6且每6环最多有一个弦的有符号平面图是Δ-edge-colorable。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An adjacency lemma on signed edge colorings with an application to planar graphs
In the study of edge colorings of graphs, critical graphs are of particular importance. One classical result concerning the structure of critical graphs is known as Vizing’s Adjacency Lemma. This lemma provides useful structural information about the neighborhood of a vertex in a critical graph. Zhang introduced an adjacency lemma dealing with the second neighborhood of a vertex in a critical graph. Both of these adjacency lemmas are useful tools for proving classification results on edge colorings. In this paper, we present an adjacency lemma on critical signed graphs with even maximum degree. This new adjacency lemma can be interpreted as a local extension of Zhang’s Adjacency Lemma. As an application of the new lemma, we show that a signed planar graph with maximum degree Δ6 in which every 6-cycle has at most one chord is Δ-edge-colorable.
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来源期刊
Discrete Applied Mathematics
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.
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