2017/01/09 by Márton Naszódi, Naszódi, Márton, Leonardo Martínez-Sandoval +3
Computer Science · Mathematics · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Computer and information sciences #Point processes and geometric inequalities #cs.CG
paper · pdf · doi:10.48550/arxiv.1701.02200
5 pages, 4 figures, EuroCG 2017
openalex publication_date 2017/01/09 · arxiv created 2017/04/20 · arxiv updated 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the following local-to-global phenomenon: Let B and R be two finite sets of (blue and red) points in the Euclidean plane ℝ2. Suppose that in each "neighborhood" of a red point, the number of blue points is at least as large as the number of red points. We show that in this case the total number of blue points is at least one fifth of the total number of red points. We also show that this bound is optimal and we generalize the result to arbitrary dimension and arbitrary norm using results from Minkowski arrangements.