二界平面图及其以外的奇着色

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-09-16 DOI:10.1016/j.dam.2025.08.064

Weichan Liu , Mengke Qi , Xin Zhang

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引用次数: 0

摘要

本文引入了二维平面图的概念。如果图形在平面上有一个嵌入，使得所有顶点位于最多两个面的边界上，并且没有任何边交叉，则该图形是双边界平面。图的适当着色是奇数，如果每个非孤立顶点都有某种颜色在其邻域上出现奇数次。Petruševski和Škrekovski在2022年推测，每个平面图形都允许奇数五色。我们在二边界平面图上证实了这个猜想。此外，我们提出了几个关于两边界平面图的独立问题。

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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Odd coloring of 2-boundary planar graphs and beyond

In this paper, we introduce the notion of 2-boundary planar graphs. A graph is 2-boundary planar if it has an embedding in the plane so that all vertices lie on the boundary of at most two faces and no edges are crossed. A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. Petruševski and Škrekovski conjectured in 2022 that every planar graph admits an odd 5-coloring. We confirm this conjecture for 2-boundary planar graphs. Moreover, we present several questions regarding 2-boundary planar graphs that are of independent interest.

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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.