A binary-matroid analogue of a graph connectivity theorem of Jamison and Mulder

Abstract

Let G be a graph such that, whenever two vertices x and y of G are joined by three internally disjoint paths, x and y are adjacent. Jamison and Mulder determined that the set of such graphs coincides with the set of graphs that can be built from cycles and complete graphs via 1-sums and parallel connections. This paper proves an analogous result for binary matroids.