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Quorum Colorings of Graphs
Let be a graph. A partition of the vertices of into {\it color classes} , with , is called a {\it quorum coloring} if for every vertex , at least half of the vertices in the closed neighborhood of have the same color as . 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