Straight line embeddings of rooted star forests in the plane

For every 1 less than or equal to i less than or equal to n, let T-i be a r ooted star with root nu i, where nu i is not necessarily its center. Then t he union F = T-1 boolean OR T-2 boolean OR . . . boolean OR T-n called a ro oted star forest with roots nu(1), nu(2), . . . , nu(n). Let P be a set of \F\ points in the plane in general position containing n specified points p (1), p(2), . . . , p(n), where \F\ denotes the order of F. Then we show tha t there exists a bijection phi : V(F) --> P such that phi(nu(i)) = p(i) for all 1 less than or equal to i less than or equal to n, phi(x) and phi(y) a re joined by a straight-line segment if and only if x and y are joined by a n edge of F, and such that no two straight-line segments intersect except a t their common end-point. (C) 2000 Elsevier Science B.V. All rights reserve d.