Acyclic domination on bipartite permutation graphs

Authors:
Guangjun Xu;Liying Kang;Erfang Shan
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, China;Department of Mathematics, Shanghai University, Shanghai, China;Department of Mathematics, Shanghai University, Shanghai, China
Venue:
Information Processing Letters
Year:
2006

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Abstract

For a graph G = (V, E), a subset S ⊆ V is called an acyclic dominating set of G if every vertex in V - S is adjacent to at least one vertex in S and the subgraph induced by S contains no cycles. In this paper, we present a linear time algorithm for transforming a minimum dominating set in a bipartite permutation graph into a minimum acyclic dominating set. Chao et al. gave a linear time algorithm to find a minimum dominating set of a permutation graph. Thus, we show that the acyclic domination problem is linear time solvable for bipartite permutation graphs.