Straight-line embeddings of two rooted trees in the plane

We prove the following theorem: Let T-1 and T-2 be two disjoint rooted tree s with roots v(1) and v(2), respectively, and let P be a set of \T1 boolean OR T-2\ points in the plane in general position containing two specified p oints p(1) and p(2) Then the union T-1 boolean OR T-2 can be straight-line embedded onto P such that v(1) and v(2) correspond to p(1) and p(2), respec tively. Moreover, we give a O (n(2) log n) time algorithm for finding such an embedding, where n is the number of vertices contained in T-1 boolean OR T-2.