平面图的弱动态着色

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。

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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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