Graphs and Matroids - Nathan Bowler

Title: Circuit partitions of finitary binary matroids

Abstract: Nash-Williams showed in 1960 that a (possibly infinite) graph can be expressed as a union of edge-disjoint cycles if and only if it has no odd cut. Recently, Joó extended this result to directed graphs, showing that a directed graph can be expressed as a union of edge-disjoint directed cycles if and only if every cut contains the same number of edges in each direction. We extend these results to finitary binary matroids. This is joint work with Attila Joó.