No Selection Lemma for Empty Triangles

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

doi:10.1007/978-3-030-83823-2_115

No Selection Lemma for Empty Triangles

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

Institute of Software Technology (7160)

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-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 language	English
Title of host publication	Trends in Mathematics
Subtitle of host publication	Extended Abstracts EuroComb 2021
Pages	720-725
Number of pages	6
DOIs	https://doi.org/10.1007/978-3-030-83823-2_115
Publication status	Published - 2021
Event	European Conference on Combinatorics, Graph Theory and Applications: EuroComb 2021 - Online, Virtual, Barcelona, Spain Duration: 6 Sept 2021 → 10 Sept 2021

Publication series

Name	Trends in Mathematics
Volume	14
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Conference

Conference	European Conference on Combinatorics, Graph Theory and Applications
Country/Territory	Spain
City	Virtual, Barcelona
Period	6/09/21 → 10/09/21

Keywords

Combinatorial geometry
Empty triangles
Horton sets
Selection Lemma
Squared Horton sets

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-030-83823-2_115

Cite this

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title = "No Selection Lemma for Empty Triangles",

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. ",

keywords = "Combinatorial geometry, Empty triangles, Horton sets, Selection Lemma, Squared Horton sets",

author = "Ruy Fabila-Monroy and Carlos Hidalgo-Toscano and Daniel Perz and Birgit Vogtenhuber",

year = "2021",

doi = "10.1007/978-3-030-83823-2_115",

language = "English",

series = "Trends in Mathematics",

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note = "European Conference on Combinatorics, Graph Theory and Applications : EuroComb 2021 ; Conference date: 06-09-2021 Through 10-09-2021",

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T1 - No Selection Lemma for Empty Triangles

AU - Fabila-Monroy, Ruy

AU - Hidalgo-Toscano, Carlos

AU - Perz, Daniel

AU - Vogtenhuber, Birgit

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Combinatorial geometry

KW - Empty triangles

KW - Horton sets

KW - Selection Lemma

KW - Squared Horton sets

UR - http://www.scopus.com/inward/record.url?scp=85114093679&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-83823-2_115

DO - 10.1007/978-3-030-83823-2_115

M3 - Chapter

T3 - Trends in Mathematics

SP - 720

EP - 725

BT - Trends in Mathematics

T2 - European Conference on Combinatorics, Graph Theory and Applications

Y2 - 6 September 2021 through 10 September 2021

ER -

No Selection Lemma for Empty Triangles

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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