1996/03/08 by János Pach, Pach, János · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.math/9603211
openalex publication_date 1996/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let P1, P2,…, Pd+1 be pairwise disjoint n-element point sets in general position in d-space. It is shown that there exist a point O and suitable subsets Qi⊆ Pi (i=1, 2, …, d+1) such that |Qi|≥ cd|Pi|, and every d-dimensional simplex with exactly one vertex in each Qi contains O in its interior. Here cd is a positive constant depending only on d.