GD 2005: Graph Drawing pp 111-116

# How to Embed a Path onto Two Sets of Points

• Emilio Di Giacomo
• Giuseppe Liotta
• Francesco Trotta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

## Abstract

Let R and B be two sets of points such that the points of R are colored red and the points of B are colored blue. Let P be a path such that |R| vertices of P are red and |B| vertices of P are blue. We study the problem of computing a crossing-free drawing of P such that each blue vertex is represented as a point of B and each red vertex of P is represented as a point of R. We show that such a drawing can always be realized by using at most one bend per edge.

### References

1. 1.
Abellanas, M., Garcia-Lopez, J., Hernández-Peñver, G., Noy, M., Ramos, P.A.: Bipartite embeddings of trees in the plane. Discrete Applied Mathematics 93(2-3), 141–148 (1999)
2. 2.
Akiyama, J., Urrutia, J.: Simple alternating path problem. Discrete Mathematics 84, 101–103 (1990)
3. 3.
Di Giacomo, E., Didimo, W., Liotta, G., Wismath, S.K.: Book-embeddability of series-parallel digraphs. Algorithmica (to appear)Google Scholar
4. 4.
Kaneko, A., Kano, M., Suzuki, K.: Path coverings of two sets of points in the plane. In: Pach, J. (ed.) Towards a Theory of Geometric Graph. Contempory Mathematics, vol. 342. American Mathematical Society, Providence (2004)Google Scholar
5. 5.
Kanenko, A., Kano, M.: Discrete geometry on red and blue points in the plane - a survey. In: Discrete and Computational Geometry. Algorithms and Combinatories, vol. 25. Springer, Heidelberg (2003)Google Scholar
6. 6.
Kaufmann, M., Wiese, R.: Embedding vertices at points: Few bends suffice for planar graphs. Journal of Graph Algorithms and Applications 6(1), 115–129 (2002)

## Copyright information

© Springer-Verlag Berlin Heidelberg 2006

## Authors and Affiliations

• Emilio Di Giacomo
• 1
• Giuseppe Liotta
• 1
• Francesco Trotta
• 1
1. 1.Dipartimento di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di Perugia