No Selection Lemma for Empty Triangles

Ruy Fabila-Monroy, Carlos Hidalgo-Toscano, Daniel Perz, Birgit Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this paper we show that for any integer n and real number 0 ≤ α≤ 1 there exists a point set of size n with Θ(n 3 - α) empty triangles such that any point of the plane is in O(n 3 - 2 α) empty triangles.

Original languageEnglish
Title of host publicationTrends in Mathematics
Subtitle of host publicationExtended Abstracts EuroComb 2021
Pages720-725
Number of pages6
DOIs
Publication statusPublished - 2021
EventEuropean Conference on Combinatorics, Graph Theory and Applications: EuroComb 2021 - Online, Virtual, Barcelona, Spain
Duration: 6 Sep 202110 Sep 2021

Publication series

NameTrends in Mathematics
Volume14
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

ConferenceEuropean Conference on Combinatorics, Graph Theory and Applications
Country/TerritorySpain
CityVirtual, Barcelona
Period6/09/2110/09/21

Keywords

  • Combinatorial geometry
  • Empty triangles
  • Horton sets
  • Selection Lemma
  • Squared Horton sets

ASJC Scopus subject areas

  • Mathematics(all)

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