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Journal of Combinatorial Optimization

, Volume 29, Issue 1, pp 247–256 | Cite as

Tractable connected domination for restricted bipartite graphs

  • Tian Liu
  • Zhao Lu
  • Ke Xu
Article

Abstract

Connected domination, i.e. the problem of finding a minimum connected dominating set in a graph, was known to be \(\mathcal {NP}\)-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.

Keywords

Connected domination Polynomial-time Circular-convex bipartite graph Triad-convex bipartite graph  Convex bipartite graph 

Notes

Acknowledgments

Thanks are due to Professor Kaile Su for encouragements and supports, to Professor Francis Y. L. Chin for bringing our attention to the notion of circular convex bipartite graphs during FAW-AAIM 2011, and to anonymous referees whose comments are very helpful to improve our presentations. Partially supported by National 973 Program of China (Grant No. 2010CB328103), Natural Science Foundation of China (Grant Nos. 61370052 and 61370156), and State Key Laboratory of Software Development Environment Open Fund (Grant No. SKLSDE-2012KF-06).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer SciencePeking UniversityBeijing China
  2. 2.National Lab of Software Development EnvironmentBeihang UniversityBeijing China

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