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Maximum Edge Bicliques in Tree Convex Bipartite Graphs

  • Hao Chen
  • Tian LiuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

We show that the computational complexity of the maximum edge biclique (MEB) problem in tree convex bipartite graphs depends on the associated trees. That is, MEB is \(\mathcal {NP}\)-complete for star convex bipartite graphs, but polynomial time solvable for tree convex bipartite graphs whose associated trees have a constant number of leaves. In particular, MEB is polynomial time solvable for triad convex bipartite graphs. Moreover, we show that the same algorithm strategy may not work for circular convex bipartite graphs, and triad convex bipartite graphs are incomparable with respect to chordal bipartite graphs.

Keywords

Maximum edge biclique Tree convex bipartite graphs Star convex bipartite graphs Triad convex bipartite graphs \(\mathcal {NP}\)-completeness Polynomial-time 

Notes

Acknowledgments

We thank the unknown reviewers whose comments are helpful to improve our presentations.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Key Laboratory of High Confidence Software Technologies (MOE), Institute of Software, School of Electronic Engineering and Computer SciencePeking UniversityBeijingChina

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