Minor-Closed Graph Classes with Bounded Layered Pathwidth
Vida Dujmović, David Eppstein, Gwenaël Joret, Pat Morin, David R. Wood · SIAM Journal on Discrete Mathematics · 2020
We prove that a minor-closed class of graphs has bounded layered pathwidth if and only if some apex-forest is not in the class. This generalizes a theorem of Robertson and Seymour, which says that a minor-closed class of graphs has bounded pathwidth if and only if some forest is not in the class.