A Voronoi poset

1999/05/04 by Roderik Lindenbergh, Roderik C. Lindenbergh, Lindenbergh, Roderik C. · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #Topological and Geometric Data Analysis #math.CO #math.GT #math.MG

paper · pdf · doi:10.48550/arxiv.math/9905018

14 pages 4 figures

arxiv created 1999/05/04 · openalex publication_date 1999/05/04 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Given a set S of n points in general position, we consider all k-th order Voronoi diagrams on S, for k=1,...,n, simultaneously. We deduce symmetry relations for the number of faces, number of vertices and number of circles of certain orders. These symmetry relations are independent of the position of the sites in S. As a consequence we show that the reduced Euler characteristic of the poset of faces equals zero whenever n odd.

Cited by

• Separating dots with circles

Related

• The edge labeling of higher order Voronoi diagrams
• Voronoi Diagrams of Arbitrary Order on the Sphere
• The Higher-Order Voronoi Diagram of Line Segments
• Limits of Voronoi Diagrams
• On the Number of Posets