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 ) | G | 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 → ∞ , such that every graph of order n and having at least ( c ( r ) + s − 1 ) n + f r , s , t ( n ) edges contains either t disjoint K r minors or a K s , t minor.