Tutte seminar - Jim Geelen

Growth rates of minor-closed classes of matroids

Abstract:

For a minor-closed class $\cM$ of matroids, we let $h(k)$ denote the maximum number of elements of a simple rank-$k$ matroid in $\cM$. In joint work with Joseph Kung and Geoff Whittle, we proved that, if $\cM$ does not contain all simple rank-2 matroids, then $h(k)$ grows either linearly, quadratically, or exponentially. I will hopefully convince you that this is interesting and will give some details about the proof.