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Well-quasi-ordering versus clique-width

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Lozin, Vadim V., Razgon, Igor and Zamaraev, Viktor (2018) Well-quasi-ordering versus clique-width. Journal of Combinatorial Theory, Series B, 130 . pp. 1-18. doi:10.1016/j.jctb.2017.09.012 ISSN 0095-8956.

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Official URL: http://dx.doi.org/10.1016/j.jctb.2017.09.012

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Abstract

Does well-quasi-ordering by induced subgraphs imply bounded clique-width for hereditary classes? This question was asked by Daligault, Rao, and Thomassé [7]. 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: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Graph theory
Journal or Publication Title: Journal of Combinatorial Theory, Series B
Publisher: Academic Press
ISSN: 0095-8956
Official Date: May 2018
Dates:
DateEvent
May 2018Published
2 October 2017Available
25 September 2017Accepted
Volume: 130
Page Range: pp. 1-18
DOI: 10.1016/j.jctb.2017.09.012
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 9 October 2017
Date of first compliant Open Access: 2 October 2018
Funder: Engineering and Physical Sciences Research Council (EPSRC)
Grant number: EP/L020408/1

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