A counterexample regarding labelled well-quasi-ordering

Korpelainen, Lozin, and Razgon conjectured that a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by only finitely many minimal forbidden induced subgraphs is labelled well-quasi-ordered, a notion stronger than that of \(n\)-well-quasi-order introd...

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Bibliographic Details
Published inarXiv.org
Main Authors Brignall, Robert, Engen, Michael, Vatter, Vincent
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.10.2018
Subjects
Graph theory
Graphs
Permutations
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Summary:Korpelainen, Lozin, and Razgon conjectured that a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by only finitely many minimal forbidden induced subgraphs is labelled well-quasi-ordered, a notion stronger than that of \(n\)-well-quasi-order introduced by Pouzet in the 1970s. We present a counterexample to this conjecture. In fact, we exhibit a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by finitely many minimal forbidden induced subgraphs yet is not \(2\)-well-quasi-ordered. This counterexample is based on the widdershins spiral, which has received some study in the area of permutation patterns.
ISSN:2331-8422