Unavoidable minors of large 3-connected binary matroids

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,K- n, its dual, the cycle matroid of the wheel with it spokes, or the vector matroid of the binary matrix (I-n \ J(n) - I-n), where J(n) is the n x n matrix of all ones. (C) 1996 Academic Press, Inc.