Abstract
We prove that for every [epsilon]}0 there are [alpha]}0 and n' in N such that for all n}=n' the following holds. For any two-colouring of the edges of K_n,n,n one colour contains copies of all trees T of order k{=(3-[epsilon])n/2 and with maximum degree {=n^[alpha].
This answers a conjecture of Schelp.