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The Excluded Tree Minor Theorem Revisited

par Dujmović, Vida V.;Hickingbotham, Robert;Joret, Gwenaël ;Micek, Piotr;Morin, Pat P.;Wood, David
Référence Combinatorics, probability & computing, 33, page (85-90)
Publication Publié, 2024-07-01

Article révisé par les pairs

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Résumé :

We prove that for every tree T of radius h, there is an integer c such that every T-minor-free graph is contained in H Kc for some graph H with pathwidth at most 2h-1. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and 2h-1 is the best possible bound.