We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Bounding the clique-width of H-free chordal graphs.

Brandstädt, Andreas and Dabrowski, Konrad K. and Huang, Shenwei and Paulusma, Daniël (2017) 'Bounding the clique-width of H-free chordal graphs.', Journal of graph theory., 86 (1). pp. 42-77.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Download PDF
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF (Advance online version)
Full text:(P) Proof
Available under License - Creative Commons Attribution.
Download PDF
Publisher Web site:
Publisher 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.
Date accepted:14 November 2016
Date deposited:24 November 2016
Date of first online publication:10 February 2017
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar