M. Jünger, S. Leipert, M. Percan,
Technical Report No. 2002.435 (2002).
Abstract
A clustered graph C=(G,T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G=(V,E) . Each vertex mu in T corresponds to a subset of the vertices of the graph called “cluster“. C -planarity is a natural extension of graph planarity for clustered graphs. As we triangulate a planar embedded graph so that G is still planar embedded after triangulation, we consider triangulation of a c -connected clustered graph that preserve the c -planar embedding. In this paper, we provide a linear time algorithm for triangulating c -connected c -planar embedded clustered graphs C=(G,T) so that C is still c -planar embedded after triangulation. We assume that every non-trivial cluster in C has at least two childcluster. This is the first time, this problem was investigated.