The matroids with the max-flow min-cut property

Abstract

AbstractThe max-flow min-cut theorem of Ford and Fulkerson (for undirected networks) may be regarded as a statement about the circuits and cocircuits using some fixed element of the cycle matroid of a graph. We show that, in general, a matroid has this property (in the integer form) if and only if it is binary and has no minor isomorphic to the dual of the Fano matroid