We introduce the concept of concept 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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Brandes, U., Erten, C., Fowler, J., Frati, F., Geyer, M., Gutwenger, C., … Symvonis, A. (2007). Colored simultaneous geometric embeddings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4598 LNCS, pp. 254–263). Springer Verlag. https://doi.org/10.1007/978-3-540-73545-8_26
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