最大度至多为五的平面图的平方着色
组合数学
2023-08-15 v2
摘要
图 的\textit{平方}，记为 ，是通过在 中给每一对拥有公共邻点的顶点添加一条边而得到的。本文中我们证明，对于每一个最大度至多为 的平面图 ， 允许使用至多 种颜色的正常顶点着色，这改进了侯、金、苗和赵最近得到的上界 。
引用
@article{arxiv.2308.01824,
title = {Square Coloring of Planar Graphs with Maximum Degree at Most Five},
author = {Jiani Zou and Miaomiao Han and Hong-Jian Lai},
journal= {arXiv preprint arXiv:2308.01824},
year = {2023}
}
备注
This is the second version. The preliminary version is uploaded to arxiv on Augest 2nd. After completing this paper, we learned that Kengo Aoki also proved the main result of this paper independently in arXiv:2307.16394