Universal pointsets for 2-coloured trees

Abstract

Let R and B be two sets of distinct points such that the points of R are coloured red and the points of B are coloured blue. Let G be a family of planar graphs such that for each graph in the family |R| vertices are red and |B| vertices are blue. The set R∪ B is a universal pointset for G if every graph G ∈ G has a straight-line planar drawing such that the blue vertices of G are mapped to the points of B and the red vertices of G are mapped to the points of R. In this paper we describe universal pointsets for meaningful classes of 2-coloured trees and show applications of these results to the coloured simultaneous geometric embeddability problem. © 2011 Springer-Verlag.