Well-quasi-ordering in lattice path matroids

TL;DR

This paper proves that lattice path matroids with bounded branch-width are well-quasi-ordered, highlighting a structural property that does not hold for all transversal matroids.

Contribution

It establishes that the class of lattice path matroids of bounded branch-width is well-quasi-ordered, a property not shared by transversal matroids in general.

Findings

Lattice path matroids are not well-quasi-ordered in general.

Bounded branch-width lattice path matroids are well-quasi-ordered.

Transversal matroids are not well-quasi-ordered, even with branch-width restrictions.

Abstract

Lattice path matroids form a subclass of transversal matroids and were introduced by Bonin, de Mier and Noy. Transversal matroids are not well-quasi-ordered, even when the branch-width is restricted. Though lattice path matroids are not well-quasi-ordered, we prove that lattice path matroids of bounded branch-width are well-quasi-ordered.