Restricted Bipartite Graphs: Comparison and Hardness Results

  • Tian Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)


Convex bipartite graphs are a subclass of circular convex bipartite graphs and chordal bipartite graphs. Chordal bipartite graphs are a subclass of perfect elimination bipartite graphs and tree convex bipartite graphs. No other inclusion among them is known. In this paper, we make a thorough comparison on them by showing the nonemptyness of each region in their Venn diagram. Thus no further inclusion among them is possible, and the known complexity results on them are incomparable. We also show the \(\mathcal{NP}\)-completeness of treewidth and feedback vertex set for perfect elimination bipartite graphs.


Perfect elimination bipartite graphs tree convex bipartite graphs circular convex bipartite graphs chordal bipartite graphs convex bipartite graphs \(\mathcal{NP}\)-completeness treewidth feedback vertex set 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tian Liu
    • 1
  1. 1.Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer SciencePeking UniversityBeijingChina

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