Quorum Colorings of Graphs
Sandra M. Hedetniemi, Renu C. Laskar, Stephen T. Hedetniemi, Henry Martyn Mulder · EUR Research Repository (Erasmus University Rotterdam) · 2012
Let G = (V,E) be a graph. A partition = {V1,V2,...,Vk} of the vertex set V of G into k color classes Vi, with 1 i k, is called a quorum coloring if for every vertex v 2 V , at least half of the vertices in the closed neighborhood N[v] of v have the same color as v. In this paper we introduce the study of quorum colorings of graphs and show that they are closely related to the concept of defensive alliances in graphs. Moreover, we determine the maximum quorum coloring of a hypercube.