Minor-closed graph classes with bounded layered pathwidth

TL;DR

This paper characterizes minor-closed graph classes with bounded layered pathwidth, showing they exclude a specific apex-forest, thus generalizing a classical theorem relating pathwidth and forest exclusion.

Contribution

It extends Robertson and Seymour's theorem by establishing a precise condition for bounded layered pathwidth involving apex-forests.

Findings

A minor-closed class has bounded layered pathwidth iff it excludes some apex-forest.

Generalizes the classical result linking pathwidth and forest exclusion.

Provides a characterization that bridges layered pathwidth and minor-closed classes.

Abstract

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 generalises 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.