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Bounding the Clique-Width of H-free Chordal Graphs

Brandstädt, A.; Dabrowski, K.K.; Huang, S.; Paulusma, D.

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Authors

A. Brandstädt

K.K. Dabrowski

S. Huang



Abstract

A graph is H-free if it has no induced subgraph isomorphic to H. Brandstädt, Engelfriet, Le, and Lozin proved that the class of chordal graphs with independence number at most 3 has unbounded clique-width. Brandstädt, Le, and Mosca erroneously claimed that the gem and co-gem are the only two 1-vertex P4-extensions H for which the class of H-free chordal graphs has bounded clique-width. In fact we prove that bull-free chordal and co-chair-free chordal graphs have clique-width at most 3 and 4, respectively. In particular, we find four new classes of H-free chordal graphs of bounded clique-width. Our main result, obtained by combining new and known results, provides a classification of all but two stubborn cases, that is, with two potential exceptions we determine all graphs H for which the class of H-free chordal graphs has bounded clique-width. We illustrate the usefulness of this classification for classifying other types of graph classes by proving that the class of inline image-free graphs has bounded clique-width via a reduction to K4-free chordal graphs. Finally, we give a complete classification of the (un)boundedness of clique-width of H-free weakly chordal graphs.

Citation

Brandstädt, A., Dabrowski, K., Huang, S., & Paulusma, D. (2017). Bounding the Clique-Width of H-free Chordal Graphs. Journal of Graph Theory, 86(1), 42-77. https://doi.org/10.1002/jgt.22111

Journal Article Type Article
Acceptance Date Nov 14, 2016
Online Publication Date Feb 10, 2017
Publication Date Feb 10, 2017
Deposit Date Nov 18, 2016
Publicly Available Date Mar 28, 2024
Journal Journal of Graph Theory
Print ISSN 0364-9024
Electronic ISSN 1097-0118
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 86
Issue 1
Pages 42-77
DOI https://doi.org/10.1002/jgt.22111
Public URL https://durham-repository.worktribe.com/output/1370015

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Copyright Statement
© 2017 Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.







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