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    Well-quasi-ordering versus clique-width

    Lozin, V. and Razgon, Igor and Zamaraev, V. (2018) Well-quasi-ordering versus clique-width. Journal of Combinatorial Theory Series B 130 , pp. 1-18. ISSN 0095-8956.

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    Does well-quasi-ordering by induced subgraphs imply bounded clique-width for hereditary classes? This question was asked by Daligault, Rao, and Thomass ́e [Well-quasi-order of relabel functions. Order, 27(3) (2010), 301–315]. We answer this question negatively by presenting a hereditary class of graphs of unbounded clique-width which is well-quasi-ordered by the induced subgraph relation. We also show that graphs in our class have at most logarithmic clique-width and that the number of minimal forbidden induced subgraphs for our class is infinite. These results lead to a conjecture relaxing the above question and to a number of related open questions connecting well-quasi-ordering and clique-width.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Igor Razgon
    Date Deposited: 22 Jan 2018 15:02
    Last Modified: 09 Aug 2023 12:42


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