We show that any planar drawing of a forest of three stars whose vertices are constrained to be at fixed vertex locations may require Ω(n2/3) edges each having Ω (n1/3) bends in the worst case. The lower bound holds even when the function that maps vertices to points is not a bijection but it is defined by a 3-coloring. In contrast, a constant number of bends per edge can be obtained for 3-colored paths and for 3-colored caterpillars whose leaves all have the same color. Such results answer to a long standing open problem.
CITATION STYLE
Di Giacomo, E., Gasieniec, L., Liotta, G., & Navarra, A. (2018). Colored point-set embeddings of acyclic graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10692 LNCS, pp. 413–425). Springer Verlag. https://doi.org/10.1007/978-3-319-73915-1_32
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