Linear-time algorithm for the matched-domination problem in cographs

Abstract

Let G=(V, E) be a graph without isolated vertices. A matching in G is a set of independent edges in G. A perfect matching M in G is a matching such that every vertex of G is incident to an edge of M. A set S⊆ V is a paired-dominating set of G if every vertex not in S is adjacent to a vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination problem is to find a paired-dominating set of G with minimum cardinality. This paper introduces a generalization of the paired-domination problem, namely, the matched-domination problem, in which some constrained vertices are in paired-dominating sets as far as they can. Further, possible applications are also presented. We then present a linear-time constructive algorithm to solve the matched-domination problem in cographs.† †A preliminary version of this paper has appeared in: Proceedings of the 4th IASTED International Conference on Computational Intelligence (CI’2009), Honolulu, Hawaii, USA, 2009, pp. 120–126.