Colored simultaneous geometric embeddings
Fowler, J. Joseph
Kobourov, Stephen G.
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CitationBrandes, U., Erten, C., Fowler, J., Frati, F., Geyer, M., Gutwenger, C., . . . & Symvonis, A. (2007). Colored simultaneous geometric embeddings. Paper presented at the Computing And Combinatorics, Proceedings, 4598, 254-263.doi:10.1007/978-3-540-73545-8_26
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.