‟Closed Neighborhood Balanced Colorings of Graphs” by Brad Fox, with Karen Collins, Bryan Freyberg, Alison Marr, et al
Abstract:
For a graph G, a neighborhood balanced coloring is a coloring of the vertices using red and blue such that each vertex has an equal number of red and blue vertices in its neighborhood. We introduce a variation called a closed neighborhood balanced coloring in which each closed neighborhood (which includes the vertex itself) has an equal number of red and blue vertices. A graph is closed neighborhood balanced colorable (CNBC) if such a coloring exists. In this talk, we will discuss various families of CNBC graphs, focusing on trees and classes relating to graph products.