极大外平面图的奇4着色

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-08 DOI:10.1016/j.disc.2025.114556

Masaki Kashima , Shun-ichi Maezawa , Kakeru Osako , Kenta Ozeki , Shoichi Tsuchiya

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引用次数: 0

摘要

图G的奇着色是具有以下性质的真着色：对于G的每一个顶点v，存在一个颜色i使得在v的邻域中有奇数个颜色i的顶点。Caro, Petruševski， Škrekovski证明了每一个外平面图都允许一个奇5着色。因为长度为5的循环不允许奇数4着色，所以这个结果是最好的。本文证明了每一个极大的外平面图都存在奇4着色。我们还展示了list版本的保存。

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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An odd 4-coloring of a maximal outerplanar graph

An odd coloring of a graph G is a proper coloring with the following property: For every vertex v of G, there exists a color i such that there are an odd number of vertices of color i in the neighborhood of v. Caro, Petruševski, and Škrekovski proved that every outerplanar graph admits an odd 5-coloring. Since the cycle of length 5 does not admit an odd 4-coloring, this result is best possible. In this paper, we prove that every maximal outerplanar graph admits an odd 4-coloring. We also show that the list version holds.

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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.