Bichromatic point-set embeddings of trees with fewer bends (Extended Abstract)

Abstract

Let G be a planar graph such that each vertex of G is colored by either red or blue color. Assume that there are nr red vertices and n b blue vertices in G. Let S be a set of fixed points in the plane such that |S| = n r + n b where nr points in S are colored by red color and nb points in S are colored by blue color. A bichromatic point-set embedding of G on S is a crossing free drawing of G such that each red vertex of G is mapped to a red point in S, each blue vertex of G is mapped to a blue point in S, and each edge is drawn as a polygonal curve. In this paper, we study the problem of computing bichromatic point-set embeddings of trees on two restricted point-sets which we call "ordered point-set" and "properly-colored point-set". We show that trees have bichromatic point-set embeddings on these two special types of point-sets with at most one bend per edge and such embeddings can be found in linear time. © 2014 Springer International Publishing Switzerland.