平面图与局部平面图的弱简并

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-11-03 DOI:10.37236/11749

Ming Han, Tao Wang, Jianglin Wu, Huan Zhou, Xuding Zhu

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引用次数: 3

摘要

弱简并是简并的一种变体，它具有简并的许多优良性质。特别地，如果一个图$G$是弱$d$-退化的，那么对于$G$的任意$(d+1)$-列表赋值$L$，可以用一种改进的贪心着色算法构造$G$的$L$着色。已知周长为5的平面图是3-可选的，局部平面图是5 -可选的。本文加强了这些结果，证明了周长为5的平面图是弱2-简并的，局部平面图是弱4-简并的。

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 Degeneracy of Planar Graphs and Locally Planar Graphs

Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d+1)$-list assignment $L$ of $G$, one can construct an $L$ coloring of $G$ by a modified greedy coloring algorithm. It is known that planar graphs of girth 5 are 3-choosable and locally planar graphs are $5$-choosable. This paper strengthens these results and proves that planar graphs of girth 5 are weakly 2-degenerate and locally planar graphs are weakly 4-degenerate.

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.