How to Embed a Path onto Two Sets of Points
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.
KeywordsPlanar Graph Blue Point Discrete Apply Mathematic Planar Drawing Rightmost Point
- 3.Di Giacomo, E., Didimo, W., Liotta, G., Wismath, S.K.: Book-embeddability of series-parallel digraphs. Algorithmica (to appear)Google Scholar
- 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.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