On minor-minimally 3-connected binary matroids

A matroid M is called minor-minimally 3-connected if M is 3-connected and, for each e ∈ E ( M ) , either M ∖ e or M / 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.