The Erdos-Posa property for clique minors in highly connected graphs

We prove the existence of a function f:N-2 -> N such that, for all p, k is an element of N, every (k(p - 3) + 14p + 14)-connected graph either has k disjoint K-p-minors or contains a set of at most f(p, k) vertices whose deletion kills all its K-p-minors. For fixed p >= 5, the connectivity bound of about k(p - 3) is smallest possible, up to an additive constant: if we assume less connectivity in terms of k, there will be no such function f. (C) 2011 Published by Elsevier Inc.