No Selection Lemma for Empty Triangles

R. Fabila-Monroy, C. Hidalgo-Toscano, D. Perz, and B. Vogtenhuber

Abstract:

In this paper we show that for any integer $n$ and real number $0\leq \alpha \leq 1$ there exists a point set of size $n$ with $\Theta(n^{3-\alpha})$ empty triangles such that any point of the plane is in $O(n^{3-2\alpha})$ empty triangles.

Reference: R. Fabila-Monroy, C. Hidalgo-Toscano, D. Perz, and B. Vogtenhuber. No selection lemma for empty triangles. In J. Nešetril, G. Perarnau, J. Rué, and O. Serra, editors, Extended Abstracts EuroComb 2021, pages 720-725, Cham, 2021. Springer International Publishing.