A new minor-closed class of transversal matroids

TL;DR

This paper introduces path-circular matroids, a new class of transversal matroids that generalize bicircular and multi-path matroids, based on a characterization of single-element contractions.

Contribution

It provides a characterization for when a contraction of a transversal matroid remains transversal and defines a new minor-closed class called path-circular matroids.

Findings

Path-circular matroids generalize bicircular and multi-path matroids.

A characterization of when a contraction of a transversal matroid is transversal.

Introduction of a new minor-closed class of transversal matroids.

Abstract

We provide a characterisation of when a single-element contraction of a transversal matroid is itself transversal. Using this characterisation, we define a new class of transversal matroids closed under minors, which we call path-circular matroids. Path-circular matroids generalise both of the well-known classes of bicircular matroids and multi-path matroids.