Bounding the Clique-Width of H-free Chordal Graphs

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

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: Nov 24, 2016
• 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