Unavoidable Minors of Large 3-Connected Binary Matroids

Abstract

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 × n matrix of all ones.