Abstract
A set D⊆V of a graph G=(V,E) is called a dominating set of G if every vertex in V∖D has at least one neighbor in D. A dominating set D of G is a paired-dominating set of G if G[D], the subgraph of G induced by D, has a perfect matching. Given a graph G, Min-Paired-Dom-Set is the problem to find a paired-dominating set of G of minimum cardinality. Min-Paired-Dom-Set is known to be NP-hard for general graphs and many other restricted classes of graphs. However, Min-Paired-Dom-Set is solvable in polynomial time in some graph classes including strongly chordal graphs and chordal bipartite graphs. In this paper, we strengthen this result by proposing a polynomial time algorithm to compute a minimum paired-dominating set in the class of strongly orderable graphs, which includes strongly chordal graphs and chordal bipartite graphs. The algorithm runs in linear time if a quasi-simple elimination ordering of the strongly orderable graph is provided.
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