NP-completeness and APX-completeness of restrained domination in graphs

Authors:
Lei Chen;Weiming Zeng;Changhong Lu
Affiliations:
College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China;College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China;Department of Mathematics, East China Normal University, Shanghai 200241, China
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

Let G=(V,E) be a simple graph. A vertex set S@?V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V-S. In this paper, we investigate the NP-completeness of the restrained domination problem in planar graphs and split graphs. Meanwhile, it is proved that the restrained domination problem is APX-complete for bounded-degree graphs.