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Paired-Domination Problem on Distance-Hereditary Graphs

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Abstract

A paired-dominating set of a graph G is a dominating set S of G such that the subgraph of G induced by S has a perfect matching. Haynes and Slater (Networks 32(3):199–206, 1998) introduced the concept of paired-domination and showed that the problem of determining minimum paired-dominating sets is NP-complete on general graphs. Ever since then many algorithmic results are studied on some important classes of graphs. In this paper, we extend the results by providing an \(O(n^2)\)-time algorithm on distance-hereditary graphs.

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Acknowledgements

This work is partially supported by the Ministry of Science and Technology under the Grants Nos. MOST 106-2221-E-019-014, and MOST 107-2221-E-019-016.

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  1. Department of Computer Science and Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan

    Ching-Chi Lin

  2. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, 10617, Taiwan

    Keng-Chu Ku & Chan-Hung Hsu

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  1. Ching-Chi Lin
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Lin, CC., Ku, KC. & Hsu, CH. Paired-Domination Problem on Distance-Hereditary Graphs. Algorithmica 82, 2809–2840 (2020). https://doi.org/10.1007/s00453-020-00705-7

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