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Complete graph minors and the graph minor structure theorem

par Joret, Gwenaël ;Wood, David
Référence Journal of combinatorial theory. Series B, 103, 1, page (61-74)
Publication Publié, 2013-01

Article révisé par les pairs

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Résumé :

The graph minor structure theorem by Robertson and Seymour shows that every graph that excludes a fixed minor can be constructed by a combination of four ingredients: graphs embedded in a surface of bounded genus, a bounded number of vortices of bounded width, a bounded number of apex vertices, and the clique-sum operation. This paper studies the converse question: What is the maximum order of a complete graph minor in a graph constructed using these four ingredients? Our main result answers this question up to a constant factor. © 2012 Gwenaël Joret and David Wood.