k-colored Point-set Embeddability of Outerplanar Graphs

Abstract

This paper addresses the problem of designing drawing algorithms that receive as input a planar graph G, a partitioning of the vertices of G into k different semantic categories V₀,…, V_k−1, and k disjoint sets S₀, …, S_k−1 of points in the plane with |V_i|=|S_i| (i ∈ {0, …,k−1}). The desired output is a planar drawing such that the vertices of V_i are mapped onto the points of S_i and such that the curve complexity of the edges (i.e. the number of bends along each edge) is kept small. Particular attention is devoted to outerplanar graphs, for which lower and upper bounds on the number of bends in the drawings are established.