Template-Type: ReDIF-Paper 1.0
Author-Name: Heditniemi, S.M.
Author-Name-Last: Heditniemi
Author-Name-First: Sandra
Author-Name: Laskar, R.C.
Author-Name-Last: Laskar
Author-Name-First: R.C.
Author-Name: Mulder, H.M.
Author-Name-Last: Mulder
Author-Name-First: Martyn
Title: Quorum Colorings of Graphs
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.
Creation-Date: 2012-09-13
File-URL: https://repub.eur.nl/pub/37620/EI2012-20.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI 2012-20
Keywords: defensive alliance, defensive alliance number, graph coloring, hypercube, neightborhood-restricted coloring, quorum coloring, quorum coloring number
Handle: RePEc:ems:eureir:37620