Let $G = (V,E)$ be a graph. A partition $\pi = \{V_1, V_2, \ldots, V_k \}$ of the vertices $V$ of $G$ into $k$ {\it color classes} $V_i$, with $1 \leq i \leq k$, is called a {\it quorum coloring} if for every vertex $v \in V$, 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.

defensive alliance, defensive alliance number, graph coloring, hypercube, neightborhood-restricted coloring, quorum coloring, quorum coloring number
Erasmus School of Economics
Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Heditniemi, S.M, Laskar, R.C, & Mulder, H.M. (2012). Quorum Colorings of Graphs (No. EI 2012-20). Report / Econometric Institute, Erasmus University Rotterdam (pp. 1–14). Erasmus School of Economics. Retrieved from http://hdl.handle.net/1765/37620