A polynomial-time algorithm for the paired-domination problem on permutation graphs

Authors:
T. C. E. Cheng;Liying Kang;Erfang Shan
Affiliations:
Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong and Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

A set S of vertices in a graph H=(V,E) with no isolated vertices is a paired-dominating set of H if every vertex of H is adjacent to at least one vertex in S and if the subgraph induced by S contains a perfect matching. Let G be a permutation graph and @p be its corresponding permutation. In this paper we present an O(mn) time algorithm for finding a minimum cardinality paired-dominating set for a permutation graph G with n vertices and m edges.