2-边界平面图及更一般图的奇着色
组合数学
2025-04-07 v2 离散数学
摘要
本文引入 2-边界平面图的概念。若一个图可嵌入平面使得所有顶点位于至多两个面的边界上且无边交叉,则称其为 2-边界平面图。图的正常着色称为奇着色,若每个非孤立顶点在其邻域中都有某种颜色出现奇数次。Petru\v{s}evski 与 \v{S}krekovski 于 2022 年猜想每个平面图均容许奇 5-着色。我们对该猜想在 2-边界平面图情形予以证实。此外,我们提出若干关于 2-边界平面图的、具有独立意义的问题。
引用
@article{arxiv.2205.09317,
title = {Odd coloring of 2-boundary planar graphs and beyond},
author = {Weichan Liu and Mengke Qi and Xin Zhang},
journal= {arXiv preprint arXiv:2205.09317},
year = {2025}
}
备注
18 pages, 5 figures. Reorganize the paper to place greater emphasis on the newly introduced 2-boundary planar graphs; incorporate various problems, questions, or conjectures related to 2-boundary planar graphs to facilitate further research; and include an additional author