A. Brandstädt
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 | 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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© 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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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
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Publisher Licence URL
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