Hybrid evolutionary algorithm for the b-chromatic number

Abstract

The b-chromatic number of a graph $$G$$G is a maximum integer $$\varphi (G)$$?(G) for which there exists a proper $$\varphi (G)$$?(G)-coloring with the additional property that each color class contains a vertex that is adjacent to one of the vertices within each color class. In contrast to many theoretical results discovered over the last decade and a half there are no computer running experiments on $$\varphi (G)$$?(G) in the literature. This work presents a hybrid evolutionary algorithm for graph b-coloring. Its performance has been tested on some instances of regular graphs where their b-chromatic number is theoretically known in advance, as well as by comparing with a brute force algorithm solving the regular graphs up to 12 vertices. In addition, the algorithm has been tested on some larger graphs taken from a DIMACS challenge benchmark that also proved to be challenging for the algorithms searching for the classical chromatic number $$\chi (G)$$?(G).