Tutte seminar - Peter Nelson

Growth Rates in Minor-Closed Classes of Matroids

Abstract:

A result of Mader states that in a proper minor-closed class of graphs, the number of edges of a graph in the class is at most linear in its number of vertices - this result gives the first glimpse of a rich structural theory of minor-closed classes of graphs famously developed by Robertson and Seymour. Analogously to this result of Mader, the 'Growth Rate Theorem' gives similar density bounds for minor-closed classes of matroids. I will discuss this theorem, along with refinements and generalisations.