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 \(M \backslash L_1\) and \(M \backslash L_2\) are connected. Our result extends the corresponding result of Kriesell regarding critically \(2\)-connected graphs.