Unavoidable minors of large 3-connected binary matroids (Q1924132)

We show that, for every integer \(n\) greater than two, there is a number \(N\) such that every 3-connected binary matroid with at least \(N\) elements has a minor that is isomorphic to the cycle matroid of \(K_{3,n}\), its dual, the cycle matroid of the wheel with \(n\) spokes, or the vector matroid of the binary matrix \((I_n |J_n - I_n)\), where \(J_n\) is the \(n \times n\) matrix of all ones.