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.
Work on this paper began at the BICI Workshop on Graph Drawing, held in Bertinoro, Italy in March 2006.
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Brandes, U. et al. (2007). Colored Simultaneous Geometric Embeddings. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_26
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DOI: https://doi.org/10.1007/978-3-540-73545-8_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73544-1
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