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 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.
Citation
Brandstädt, A., Dabrowski, K., Huang, S., & 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 (139-150). https://doi.org/10.1007/978-3-662-48054-0_12
Conference Name | 40th International Symposium, MFCS 2015 |
---|---|
Conference Location | Milan, Italy |
Publication Date | Aug 11, 2015 |
Deposit Date | Aug 12, 2015 |
Publicly Available Date | Aug 11, 2016 |
Pages | 139-150 |
Series Title | Lecture notes in computer science |
Series Number | 9235 |
Series ISSN | 0302-9743 |
Book Title | Mathematical foundations of computer science 2015 : 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, proceedings, part II. |
ISBN | 9783662480533 |
DOI | https://doi.org/10.1007/978-3-662-48054-0_12 |
Public URL | https://durham-repository.worktribe.com/output/1152234 |
Additional Information | Conference dates: August 24-28, 2015, |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-48054-0_12
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