Graphs and Matroids - Mathieu Rundstrom

Title:Almost Regular Matroids

Abstract: Regular matroids form an important and extensively studied class of matroids and have numerous known descriptions and characterizations. In the 1980s, Truemper gave a constructive description of the related class of almost regular matroids: non-regular matroids $M$ such that for every element $e$ of $M$ either $M/e$ or $M\backslash e$ is regular. In this talk, we present a description of almost regular matroids in terms of grafts. A consequence of this description is that almost regular matroids have bounded complexity. We outline some of the proof ideas after introducing the necessary background.