平面图的弱动态着色

IF 0.6 4区数学 Q3 MATHEMATICS

Graphs and Combinatorics Pub Date : 2024-02-24 DOI:10.1007/s00373-023-02748-3

Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger

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引用次数: 0

摘要

图 G 的 k 弱动态数是我们为 G 的顶点着色所需的最小颜色数，即每个度数为 d(v)的顶点 v 在其邻域上看到的颜色至少为 min(\{k,d(v)\}\)。我们使用可还原配置和图的列表着色来证明所有平面图的 3 弱动态数最多为 6。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Weak Dynamic Coloring of Planar Graphs

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Weak Dynamic Coloring of Planar Graphs

The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min\(\{k,d(v)\}\) colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.

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来源期刊

Graphs and Combinatorics 数学-数学

CiteScore

1.00

自引率

14.30%

发文量

160

审稿时长

6 months

期刊介绍： Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.