Unavoidable Minors of Large 2- and 3-Connected Matroids

Abstract

It is well known that every sufficiently large 2-connected loopless graph has a big cycle or a big bond. Twenty years ago, at the Seattle Graph Minors Conference, Robin Thomas asked whether the analogous result is true for 2-connected matroids. During that meeting, Schrijver, Seymour, and Lovasz answered the question affirmatively. This talk will survey results in this area, the most recent of which relate to capturing small sets of elements in large unavoidable minors.