Sets of points determining only acute angles and some related colouring problems

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
LanguageEnglish
Article numberR12
Number of pages24
JournalThe Electronic Journal of Combinatorics
Volume13
Issue number1
Publication statusPublished - 15 Feb 2006

Fingerprint

Acute angle
Coloring
Set of points
Colouring
Lower bound
Acute
Angle
Integer

Keywords

  • point sets
  • probabilistic method
  • acute angles

Cite this

@article{a12d07b1045c493e8e017cb0953e4a06,
title = "Sets of points determining only acute angles and some related colouring problems",
abstract = "We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and F{\"u}redi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.",
keywords = "point sets, probabilistic method, acute angles",
author = "David Bevan",
year = "2006",
month = "2",
day = "15",
language = "English",
volume = "13",
journal = "The Electronic Journal of Combinatorics",
issn = "1077-8926",
number = "1",

}

Sets of points determining only acute angles and some related colouring problems. / Bevan, David.

In: The Electronic Journal of Combinatorics, Vol. 13, No. 1, R12, 15.02.2006.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Sets of points determining only acute angles and some related colouring problems

AU - Bevan, David

PY - 2006/2/15

Y1 - 2006/2/15

N2 - We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.

AB - We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.

KW - point sets

KW - probabilistic method

KW - acute angles

UR - http://www.combinatorics.org/

UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v13i1r12

M3 - Article

VL - 13

JO - The Electronic Journal of Combinatorics

T2 - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

M1 - R12

ER -