Well-quasi-ordering versus clique-width: new results on bigenic classes

Dabrowski, K.K.; Lozin, V.V.; Paulusma, D.

Abstract

Daligault, Rao and Thomassé asked whether a hereditary class of graphs well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this is not true for classes defined by infinitely many forbidden induced subgraphs. However, in the case of finitely many forbidden induced subgraphs the question remains open and we conjecture that in this case the answer is positive. The conjecture is known to hold for classes of graphs defined by a single forbidden induced subgraph H, as such graphs are well-quasi-ordered and are of bounded clique-width if and only if H is an induced subgraph of P4. For bigenic classes of graphs, i.e. ones defined by two forbidden induced subgraphs, there are several open cases in both classifications. In the present paper we obtain a number of new results on well-quasi-orderability of bigenic classes, each of which supports the conjecture.

Citation

Dabrowski, K., Lozin, V., & Paulusma, D. (2018). Well-quasi-ordering versus clique-width: new results on bigenic classes. Order, 35(2), 253-274. https://doi.org/10.1007/s11083-017-9430-7

• Journal Article Type: Article
• Acceptance Date: May 13, 2017
• Online Publication Date: Jun 29, 2017
• Publication Date: Jul 1, 2018
• Deposit Date: May 20, 2017
• Publicly Available Date: May 23, 2017
• Journal: Order
• Print ISSN: 0167-8094
• Electronic ISSN: 1572-9273
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 35
• Issue: 2
• Pages: 253-274
• DOI: https://doi.org/10.1007/s11083-017-9430-7
• Public URL: https://durham-repository.worktribe.com/output/1357922