On proper conflict-free colorings of IC-planar graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-05-08 DOI:10.1016/j.dam.2025.05.005

Yali Wu, Xin Zhang

引用次数: 0

Abstract

A proper conflict-free coloring of a graph is a proper vertex coloring ensuring that for every vertex of degree at least one there exists a color that appears exactly once in its open neighborhood. An IC-planar graph is a graph that can be embedded in a plane without having any edge crossed more than once, with the condition that each vertex is linked to no more than one crossing edge. Proper conflict-free coloring has several practical applications, especially in the areas of wireless networks, frequency allocation, and scheduling problems, and IC-planarity is a powerful tool in the areas of network design, graph drawing, and visualization. This paper introduces the inaugural finding regarding the proper conflict-free coloring of IC-planar graphs, demonstrating that any such graph can be properly conflict-free colored with no more than 20 colors.

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ic平面图的适当无冲突着色

图的适当的无冲突着色是一种适当的顶点着色，确保对于每个至少为1度的顶点存在一种在其开放邻域中恰好出现一次的颜色。ic平面图是一种可以嵌入到平面中而不需要任何边交叉一次以上的图，其条件是每个顶点连接到不超过一个交叉边。适当的无冲突着色有几个实际应用，特别是在无线网络、频率分配和调度问题领域，ic平面性是网络设计、图形绘制和可视化领域的强大工具。本文介绍了ic -平面图的适当无冲突着色的首次发现，证明了任意ic -平面图的适当无冲突着色不超过20种颜色。

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.