NP-Completeness of Neighborhood Balanced Colorings

TL;DR

This paper proves that deciding the existence of a Neighborhood Balanced Coloring in a graph is NP-complete and introduces a genetic algorithm to approximate solutions.

Contribution

It establishes NP-completeness for NBC and proposes a genetic algorithm as a heuristic approach.

Findings

NP-completeness of NBC established

Genetic algorithm performs competitively

Comparison with exact and randomized algorithms

Abstract

A Neighborhood Balanced Coloring (NBC) of a graph is a red-blue coloring where each vertex has the same number of red and blue neighbors. This work proves that determining if a graph admits an NBC is NP-complete. We present a genetic algorithm to solve this problem, which we implemented and compared against exact and randomized algorithms.