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Tractable connected domination for restricted bipartite graphs

Author

Listed:
  • Tian Liu

    (Peking University)

  • Zhao Lu

    (Peking University)

  • Ke Xu

    (Beihang University)

Abstract

Connected domination, i.e. the problem of finding a minimum connected dominating set in a graph, was known to be $$\mathcal {NP}$$ NP -complete for chordal bipartite graphs, but to be tractable for convex bipartite graphs. In this paper, connected domination is shown to be tractable for circular- and triad-convex bipartite graphs respectively, by efficient reductions from these graphs to convex bipartite graphs.

Suggested Citation

  • Tian Liu & Zhao Lu & Ke Xu, 2015. "Tractable connected domination for restricted bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 247-256, January.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:1:d:10.1007_s10878-014-9729-x
    DOI: 10.1007/s10878-014-9729-x
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    References listed on IDEAS

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    1. Yingshu Li & Yiwei Wu & Chunyu Ai & Raheem Beyah, 2012. "On the construction of k-connected m-dominating sets in wireless networks," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 118-139, January.
    2. M. H. Akhbari & R. Hasni & O. Favaron & H. Karami & S. M. Sheikholeslami, 2013. "On the outer-connected domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 10-18, July.
    3. Hongjie Du & Weili Wu & Shan Shan & Donghyun Kim & Wonjun Lee, 2012. "Constructing weakly connected dominating set for secure clustering in distributed sensor network," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 301-307, February.
    4. Weiping Shang & Frances Yao & Pengjun Wan & Xiaodong Hu, 2008. "On minimum m-connected k-dominating set problem in unit disc graphs," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 99-106, August.
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    Cited by:

    1. Hao Chen & Zihan Lei & Tian Liu & Ziyang Tang & Chaoyi Wang & Ke Xu, 2016. "Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 95-110, July.
    2. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 0. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    3. Henning, Michael A. & Ananchuen, Nawarat & Kaemawichanurat, Pawaton, 2020. "Traceability of connected domination critical graphs," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 2020. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 713-732, October.

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