On minor-minimally 3-connected binary matroids

A matroid MM is called minor-minimally 3-connected   if MM is 3-connected and, for each e∈E(M)e∈E(M), either M∖eM∖e or M/eM/e is not 3-connected. In this paper, we prove a chain theorem for the class of minor-minimally 3-connected binary matroids. As a consequence, we obtain a chain theorem for the class of minor-minimally 3-connected graphs.