Quorum Colorings of Graphs

Sandra Heditniemi, R.C. Laskar and Martyn Mulder

No EI 2012-20, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: 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.

Keywords: defensive alliance; defensive alliance number; graph coloring; hypercube; neightborhood-restricted coloring; quorum coloring; quorum coloring number (search for similar items in EconPapers)
Date: 2012-09-13
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