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Classifying the clique-width of H-free bipartite graphs.

Dabrowski, K.K. and Paulusma, D. (2014) 'Classifying the clique-width of H-free bipartite graphs.', in 20th International Conference, COCOON 2014, Atlanta, GA, USA, 4-6 August 2014 ; proceedings. Berlin, Heidelberg: Springer, pp. 489-500. Lecture notes in computer science. (8591).

Abstract

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 TeX or TeX. 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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/978-3-319-08783-2_42
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-08783-2_42
Date accepted:No date available
Date deposited:15 January 2015
Date of first online publication:2014
Date first made open access:No date available

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