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Clique-width for graph classes closed under complementation.

Blanché, A. and Dabrowski, K.K. and Johnson, M. and Lozin, V.V. and Paulusma, D. and Zamaraev, V. (2020) 'Clique-width for graph classes closed under complementation.', SIAM journal on discrete mathematics., 34 (2). pp. 1107-1147.

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 study 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 (H, H)-free graphs of bounded clique-width (as a side effect, this leaves only five 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 every set F of self-complementary graphs on at least five vertices, the classification of the boundedness of clique-width for ({H, H} ∪ F)-free graphs coincides with the one for the |H| = 2 case if and only if F does not include the bull

Item Type:Article
Full text:Publisher-imposed embargo
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1137/18M1235016
Publisher statement:© 2020 Society for Industrial and Applied Mathematics.
Date accepted:03 February 2020
Date deposited:05 February 2020
Date of first online publication:05 May 2020
Date first made open access:15 May 2020

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