On monochromatic triangles
type: Item
instance of: scholarly article
title: On monochromatic triangles
zbMATH Open document ID: 0545.52007
DOI: 10.1016/0097-3165(84)90072-4
author: Peter Borwein
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: The author first gives a particularly simple proof of J. B. Kelly's theorem: If A and B are two finite sets in \(R^ d\) (\(d\geq 2)\) with every open segment joining two points in the same set containing a point of the other, then all the points of A and B lie on a line. Then he generalizes to: If A and B are finite disjoint sets and A contains \(2d+1\) points in a general position then there is a d-simplex with vertices in one of the sets and no point of either set in its interior. In another theorem (in \(R^ 2)\) conditions are given that guarantee the existence of a triangle with vertices in one of the sets and no other point (from either set) on its boundary.
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 3868124
zbMATH Keywords: monochromatic triangles
zbMATH Keywords: two-colored set
zbMATH Keywords: simplex
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90072-4
OpenAlex ID: W1999574782
cites work: Generalizations of a combinatorial lemma of Kelly
cites work: Sylvester's Problem on Collinear Points and a Relative
cites work: Q5628823
description: scientific article; zbMATH DE number 3868124