Neighborhood Balanced 3-Coloring
Combinatorics
2024-10-10 v1
Abstract
A graph is said to be neighborhood 3-balanced if there exists a vertex labeling with three colors so that each vertex has an equal number of neighbors of each color. We give order constraints on 3-balanced graphs, determine which generalized Petersen and Pappus graphs are 3-balanced, discuss when being 3-balanced is preserved under various graph constructions, give two general characterizations of cubic 3-balanced graphs, and classify cubic 3-balanced graphs of small order.
Keywords
Cite
@article{arxiv.2410.05422,
title = {Neighborhood Balanced 3-Coloring},
author = {Mitchell Minyard and Mark R. Sepanski},
journal= {arXiv preprint arXiv:2410.05422},
year = {2024}
}