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, A. and Dabrowski, K.K. and Huang, S. and Paulusma, D. (2015) 'Bounding the clique-width of H-free chordal graphs.', in Mathematical foundations of computer science 2015 : 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, proceedings, part II. Berlin: Springer, pp. 139-150. Lecture notes in computer science. (9235).


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 the 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 prove that the clique-width is: (i) bounded for four classes of H-free chordal graphs; (ii) unbounded for three subclasses of split graphs. 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 (2P1+P3,K4)-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:Book chapter
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:19 August 2015
Date of first online publication:August 2015
Date first made open access:11 August 2016

Save or Share this output

Look up in GoogleScholar