论文信息 - On properties of higher-order Delaunay graphs with applications

On properties of higher-order Delaunay graphs with applications

In this work we study the order-k Delaunay graph, which is formed by edges pq having a circle through p and q and containing no more than k sites. We study the combinatorial structure of the set of triangulations that can be constructed with edges of this graph and show that it is connected under the flip operation if k ≤ 1a nd for everyk if points are in convex position. We also study the hamiltonicity of the order-k Delaunay graph and give an application to a coloring problem.

[1] Atsuyuki Okabe,et al. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[2] Sariel Har-Peled,et al. On conflict-free coloring of points and simple regions in the plane , 2003, SCG '03.

[3] Joachim Gudmundsson,et al. Constrained higher order Delaunay triangulations , 2005, Comput. Geom..

[4] E. Welzl,et al. Convex Quadrilaterals and k-Sets , 2003 .

[5] Raimund Seidel,et al. Circles through two points that always enclose many points , 1989 .

[6] Chuan Yi Tang,et al. 20-relative Neighborhood Graphs Are Hamiltonian , 1990, J. Graph Theory.

[7] Joachim Gudmundsson,et al. Higher order Delaunay triangulations , 2000, Comput. Geom..

[8] Ruei-Chuan Chang,et al. The K-Gabriel Graphs and Their Applications , 1990, SIGAL International Symposium on Algorithms.