图的闭 neighborhoods 平衡 k 着色
组合数学
2025-10-21 v1
摘要
对于简单图 G = (V, E) 及整数 k ≥ 2，若对顶点进行着色使用恰好 k 种颜色，使得每个顶点的闭 neighborhoods 中每种颜色的顶子数相等，则称该着色为闭 neighborhoods 平衡 k 着色 (closed neighborhood-balanced k-coloring)，承认具有此类着色性质的图称为闭 neighborhoods 平衡 k 着色图 (closed neighborhood balanced k-colored graph)。我们推导了图是否容许闭 neighborhoods 平衡 k 着色的若干必要条件与充分条件，并讨论了涉及此类图的各种图操作。进一步地，我们证明不存在对闭 neighborhoods 平衡 k 可着色图的 forbidden subgraph 描述。
关键词
引用
@article{arxiv.2510.16666,
title = {Closed Neighborhood Balanced k-Coloring of Graphs},
author = {Maurice Almeida and Ravindra Pawar and Siddharth Gupta and Tarkeshwar Singh},
journal= {arXiv preprint arXiv:2510.16666},
year = {2025}
}