The NP-completeness of Steiner Tree and Dominating Set for chordal bipartite graphs
Theoretical Computer Science
Labeling algorithms for domination problems in sun-free chordal graphs
Discrete Applied Mathematics
Domination in convex and chordal bipartite graphs
Information Processing Letters
Classes of bipartite graphs related to chordal graphs
Discrete Applied Mathematics
Strongly orderable graphs: a common generalization of strongly chordal and chordal bipartite graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Journal of Global Optimization
Linear Time Algorithms on Chordal Bipartite and Strongly Chordal Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Paired domination on interval and circular-arc graphs
Discrete Applied Mathematics
A polynomial-time algorithm for the paired-domination problem on permutation graphs
Discrete Applied Mathematics
A linear-time algorithm for paired-domination problem in strongly chordal graphs
Information Processing Letters
An O(n)-Time Algorithm for the Paired-Domination Problem on Permutation Graphs
Combinatorial Algorithms
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A set D⊆V of a graph G=(V,E) is a dominating set of G if every vertex in V驴D has at least one neighbor in D. A dominating set D of G is a paired-dominating set of G if the induced subgraph, G[D], has a perfect matching. Given a graph G=(V,E) and a positive integer k, the paired-domination problem is to decide whether G has a paired-dominating set of cardinality at most k. The paired-domination problem is known to be NP-complete for bipartite graphs. In this paper, we, first, strengthen this complexity result by showing that the paired-domination problem is NP-complete for perfect elimination bipartite graphs. We, then, propose a linear time algorithm to compute a minimum paired-dominating set of a chordal bipartite graph, a well studied subclass of bipartite graphs.