Classifying the Clique-Width of H-Free Bipartite Graphs

  • Konrad Kazimierz Dabrowski
  • Daniël Paulusma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)


Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (B H ,W H ). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph. Second, G is strongly H-free if G is H-free or else has no bipartition (B G ,W G ) with B H  ⊆ B G and W H  ⊆ W G . Third, G is weakly H-free if G is H-free or else has at least one bipartition (B G ,W G ) with \(B_H\not\subseteq B_G\) or \(W_H\not\subseteq W_G\). Lozin and Volz characterized all bipartite graphs H for which the class of strongly H-free bipartite graphs has bounded clique-width. We extend their result by giving complete classifications for the other two variants of H-freeness.


Bipartite Graph Graph Class Free Graph Discrete Apply Mathematic Graph Operation 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Konrad Kazimierz Dabrowski
    • 1
  • Daniël Paulusma
    • 1
  1. 1.School of Engineering and Computing SciencesDurham University, Science LaboratoriesDurhamUnited Kingdom

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