Disjoint complete minors and bipartite minors

Let r, s and t be integers and let c(r) be such that every graph G with at least c(r)vertical bar G vertical bar edges has a K-r minor. We prove that there is a function f(r,s,t)(n), with f(r,s,t)(n) = o(n) as n -> infinity, such that every graph of order it and having at least (c(r) + s -1)n + f(r,s,t) (n) edges contains either t dis joint K-r minors or a K-s,K-t minor. (C) 2006 Elsevier Ltd. All rights reserved.