2024/02/12 by Bhaswar B. Bhattacharya, Bhattacharya, Bhaswar B., Sandip Das +5
Mathematics · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2402.07775
openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a set P of n points in the plane, in general position, denote by NΔ(P) the number of empty triangles with vertices in P. In this paper we investigate by how much NΔ(P) changes if a point x is removed from P. By constructing a graph GP(x) based on the arrangement of the empty triangles incident on x, we transform this geometric problem to the problem of counting triangles in the graph GP(x). We study properties of the graph GP(x) and, in particular, show that it is kite-free. This relates the growth rate of the number of empty triangles to the famous Ruzsa-Szemerédi problem.