Colored simultaneous geometric embeddings

Authors:
U. Brandes;C. Erten;J. Fowler;F. Frati;M. Geyer;C. Gutwenger;S. Hong;M. Kaufmann;S. G. Kobourov;G. Liotta;P. Mutzel;A. Symvonis
Affiliations:
Department of Computer & Information Science, University of Konstanz;Department of Computer Science, Isik University;Department of Computer Science, University of Arizona;Department of Computer Science, University of Roma Tre;Wilhelm-Schickard-Institute of Computer Science, University of Tübingen;Department of Computer Science, University of Dortmund;NICTA Ltd. and School of Information Technologies, University of Sydney;Wilhelm-Schickard-Institute of Computer Science, University of Tübingen;Department of Computer Science, University of Arizona;School of Computing, University of Perugia;Department of Computer Science, University of Dortmund;School of Applied Math. & Phys. Sciences, National Technical University of Athens
Venue:
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Year:
2007

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Abstract

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.