On the Number of Intersections of Three Monochromatic Trees in the Plane

Abstract

Let R, B, and G be three disjoint sets of points in the plane such that the points of $X=R \cup B \cup G\phantom{}$ are in general position. In this paper, we prove that we can draw three spanning geometric trees on R, on B, and on G such that every edge intersects at most three segments of each other tree. Then the number of intersections of the trees is at most 3|X|-9. A similar problem had been previously considered for two point sets.