Abstract :
In this paper we shall show that if G = (V, E) is a bipartite graph with more than (a − 1)‖Y‖ + (b − 1)‖ X‖ − (a − 1)(b − 1) edges, where (X, Y) is a vertex-partition for G and a ⩽ b are natural numbers with a ⩽ ‖X‖, b ⩽ ‖Y‖, then G contains every tree T with bipartite-numbers a ⩽ b. This result is related to Ramsey-theory for trees.
