Outerplanar Obstructions for Matroid Pathwidth

For each k, we provide all outerplanar obstructions for the class of graphs whose cycle matroid has pathwidth at most k. Our proof combines a decomposition lemma for proving lower bounds on matroid pathwidth and a relation between matroid pathwidth and linear-width. Our results imply the existence of a linear algorithm that, given an outerplanar graph, outputs its matroid pathwidth.