On Removable Series Classes in Critically Connected Binary Matroids

Abstract

Let $M$ be a simple connected binary matroid with corank at least two such that $M$ has no connected hyperplane. Seymour proved that $M$ has a non-trivial series class. We improve this result by proving that $M$ has at least two disjoint non-trivial series classes $L_1$ and $L_2$ such that both $M\mathrm{\setminus }{L}_1$ and $M\mathrm{\setminus }{L}_2$ are connected. Our result extends the corresponding result of Kriesell regarding critically $2$-connected graphs.