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Clique-Width for Graph Classes Closed under Complementation

Blanché, A.; Dabrowski, K. K.; Johnson, M.; Lozin, V. V.; Paulusma, D.; Zamaraev, V.

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Authors

A. Blanché

K. K. Dabrowski

V. V. Lozin

V. Zamaraev



Contributors

Kim G. Larsen
Editor

Hans L. Bodlaender
Editor

Jean-Francois Raskin
Editor

Abstract

Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set H of forbidden induced subgraphs. We initiate a systematic study into the boundedness of clique-width of hereditary graph classes closed under complementation. First, we extend the known classification for the |H|=1 case by classifying the boundedness of clique-width for every set H of self-complementary graphs. We then completely settle the |H|=2 case. In particular, we determine one new class of (H1, complement of H1)-free graphs of bounded clique-width (as a side effect, this leaves only six classes of (H1, H2)-free graphs, for which it is not known whether their clique-width is bounded). Once we have obtained the classification of the |H|=2 case, we research the effect of forbidding self-complementary graphs on the boundedness of clique-width. Surprisingly, we show that for a set F of self-complementary graphs on at least five vertices, the classification of the boundedness of clique-width for ({H1, complement of H1} + F)-free graphs coincides with the one for the |H|=2 case if and only if F does not include the bull (the only non-empty self-complementary graphs on fewer than five vertices are P_1 and P_4, and P_4-free graphs have clique-width at most 2). Finally, we discuss the consequences of our results for COLOURING.

Citation

Blanché, A., Dabrowski, K. K., Johnson, M., Lozin, V. V., Paulusma, D., & Zamaraev, V. (2017). Clique-Width for Graph Classes Closed under Complementation. In K. G. Larsen, H. L. Bodlaender, & J. Raskin (Eds.), 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) : August 21-25, 2017, Aalborg (Denmark) ; proceedings. https://doi.org/10.4230/lipics.mfcs.2017.73

Conference Name 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS).
Conference Location Aalborg, Denmark
Start Date Aug 21, 2017
End Date Aug 25, 2017
Acceptance Date Jun 12, 2017
Publication Date Dec 1, 2017
Deposit Date Jul 2, 2017
Publicly Available Date Jul 3, 2017
Series Title LIPIcs–Leibniz International Proceedings in Informatics
Series Number 83
Series ISSN 1868-8969
Book Title 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) : August 21-25, 2017, Aalborg (Denmark) ; proceedings.
DOI https://doi.org/10.4230/lipics.mfcs.2017.73
Public URL https://durham-repository.worktribe.com/output/1146723

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