The excluded minors for the intersection of bicircular and lattice path matroids

Abstract

The classes of bicircular matroids and lattice path matroids are closed under minors. The complete list of excluded minors for the class of lattice path matroids is known, and it has been recently shown that the analogous list for the class of bicircular matroids is finite. In this paper, we establish the complete list of excluded minors for the class of matroids that is the intersection of these two classes. This resolves a recently posed open problem.