Majority Sets in Graphs

Chellali, Mustapha; Hedetniemi, Stephen T.; Meddah, Nacéra

doi:10.22049/cco.2025.30739.2602

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	Majority Sets in Graphs
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 آذر 1404 اصل مقاله (467.32 K)
نوع مقاله: Special issue of CCO to honor Odile Favaron
شناسه دیجیتال (DOI): 10.22049/cco.2025.30739.2602
نویسندگان
Mustapha Chellali^* ¹؛ Stephen T. Hedetniemi²؛ Nacéra Meddah¹
¹AMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria
²Professor and Chair Emeritus of Computer Science, Clemson University, Clemson, SC 29634 USA
چکیده
A set of vertices $S\subseteq V$ in a graph $G=(V,E)$ is called an internal majority set if for every vertex $v\in S$, a majority of the neighbors of $v$ are in $S$, or equivalently, every vertex $v\in S$ has fewer neighbors in $V-S=\overline{S}$ than it has in $S$. A set $S$ is called an external majority set if for every vertex $v\in\overline{S}$, a majority of the neighbors of $v$ are in $S$, or equivalently, every vertex $v\in\overline{S}$ has more neighbors in $S$ than it has in $\overline{S}$. A set of vertices $S\subseteq V$ in a graph $G=(V,E)$ is called a total majority set if for every vertex $v\in V$, a majority of the neighbors of $v$ are in $S$, or equivalently, every vertex $v\in V$ has more neighbors in $S$ than it has in $\overline{S}$. In this paper we show that majority sets in graphs are closely related to, but different than, a variety of sets that have been studied, such as offensive alliances, cost effective and very cost effective sets and unfriendly partitions in graphs. We also prove that the decision problems associated with external majority sets and total majority sets are NP-complete. Finally, we present a list of open problems related to majority sets in graphs.
کلیدواژه‌ها
minority sets, majority sets, independent sets؛ hereditary properties؛ dominating sets in graphs

مراجع
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Majority Sets in Graphs