A Fully Dynamic Distributed Algorithm for a B-Coloring of Graphs

A b-coloring of a graph G is a proper coloring of the nodes of G such that each color class contains a node that has a neighbor in all other color classes. A fully dynamic algorithm is an algorithm used to support modifications (insertion or deletion) of nodes and edges in a network. Thus, in this paper we propose a fully dynamic distributed algorithm to maintain a b-coloring of a graph when its topology evolves. This method determines a b-coloring in time O(¿²) and needs O(n¿) changes of colors to maintain a b-coloring of a graph, where n is the number of nodes and ¿ is the maximum degree in the graph.