Colored Simultaneous Geometric Embeddings

We introduce the concept of colored simultaneous geometric embeddings as a generalization of simultaneous graph embeddings with and without mapping. We show that there exists a universal pointset of size n for paths colored with two or three colors. We use these results to show that colored simultaneous geometric embeddings exist for: (1) a 2-colored tree together with any number of 2-colored paths and (2) a 2-colored outerplanar graph together with any number of 2-colored paths. We also show that there does not exist a universal pointset of size n for paths colored with five colors. We finally show that the following simultaneous embeddings are not possible: (1) three 6-colored cycles, (2) four 6-colored paths, and (3) three 9-colored paths.

• Type: Conference
• Year: 2007
• Where: COCOON
• Authors: Ulrik Brandes, Cesim Erten, J. Joseph Fowler, Fabrizio Frati, Markus Geyer, Carsten Gutwenger, Seok-Hee Hong, Michael Kaufmann, Stephen G. Kobourov, Giuseppe Liotta, Petra Mutzel, Antonios Symvonis
• Keywords: 2-colored Paths, COCOON 2007, Simultaneous Geometric Embeddings, Simultaneous Graph Embeddings