UNAVOIDABLE MINORS OF LARGE 3-CONNECTED MATROIDS

This paper proves that, for every integer n exceeding two, there is a number N(n) such that every 3-connected matroid with at least N(n) ele ments has a minor that is isomorphic to one of the Following matroids: an (n + 2)-point line or its dual, the cycle or cocycle matroid of K- 3,K-n, the cycle matroid of a wheel with n spokes, a whirl of rank n, or an n-spike. A matroid is of the last type if it has rank n and cons ists of n three-point lines through a common point such that, for all k in {1,2,..., n - 1}, the union of every set of k of these lines has rank k + 1. (C) 1997 Academic Press.