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

Author

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  • B. S. Panda

    (Indian Institute of Technology)

  • D. Pradhan

    (Indian Institute of Technology)

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.

Suggested Citation

  • B. S. Panda & D. Pradhan, 2013. "Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 26(4), pages 770-785, November.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:4:d:10.1007_s10878-012-9483-x
    DOI: 10.1007/s10878-012-9483-x
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    References listed on IDEAS

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    1. Paul Dorbec & Sylvain Gravier & Michael A. Henning, 2007. "Paired-domination in generalized claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 1-7, July.
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    Cited by:

    1. Tian Liu & Chaoyi Wang & Ke Xu, 2015. "Large hypertree width for sparse random hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 531-540, April.
    2. Ching-Chi Lin & Cheng-Yu Hsieh & Ta-Yu Mu, 2022. "A linear-time algorithm for weighted paired-domination on block graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 269-286, August.

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