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Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs

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Abstract

A set D⊆V of a graph G=(V,E) is 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 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.

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Acknowledgements

The authors would like to thank the anonymous referee for the detailed review and for the helpful and constructive comments leading to the improvements in the presentation of the paper.

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Authors and Affiliations

  1. Computer Science and Application Group, Department of Mathematics, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, 110016, India

    B. S. Panda & D. Pradhan

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  1. B. S. Panda
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  2. D. Pradhan
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Correspondence to B. S. Panda.

Additional information

The second author was supported by Council of Scientific & Industrial Research (CSIR), INDIA.

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Panda, B.S., Pradhan, D. Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs. J Comb Optim 26, 770–785 (2013). https://doi.org/10.1007/s10878-012-9483-x

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