  We prove that for all epsilon>0 there are c>0 and n_0 such that for all n>n_0
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 t<(3-epsilon)n/2 and with
maximum degree at most n^c. This confirms a conjecture of Schelp.
