Abstract
Let G be a planar graph with n vertices whose vertex set is partitioned into subsets V 0, ..., V k − 1 for a positive integer 1 ≤ k ≤ n and let S be a set of n distinct points in the plane partitioned into subsets S 0, ..., S k − 1 with |V i | = |S i | (0 ≤ i ≤ k − 1). This paper studies the problem of computing a crossing-free drawing of G such that each vertex of V i is mapped to a distinct point of S i . Lower and upper bounds on the number of bends per edge are proved for any 3 ≤ k ≤ n. As a special case, we improve the upper and lower bounds presented in a paper by Pach and Wenger for k = n [Graphs and Combinatorics (2001), 17:717–728].
This work is partially supported by the MIUR Project “MAINSTREAM: Algorithms for massive information structures and data streams”.
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Badent, M., Di Giacomo, E., Liotta, G. (2007). Drawing Colored Graphs on Colored Points. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_10
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DOI: https://doi.org/10.1007/978-3-540-73951-7_10
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