On the Erdös-diameter of sets
type: Item
instance of: scholarly article
title: On the Erdös-diameter of sets
zbMATH Open document ID: 0853.52018
DOI: 10.1016/0012-365X(95)00208-E
published in: Discrete Mathematics
publication date: 1996-09-01T00:00:00Z
review text: Let \(\delta(n)\) be the minimum diameter of a set of \(n\) points in the plane in which any two positive distances, if they are different, differ by at least one. The best general upper bound is given by \(n\) equidistant points on a line. P. Erdös conjectured that \(\delta(n) = n - 1\) for \(n\) sufficiently big. [See also \textit{A. Baker} et al., `A tribute to Paul Erdös' (1990; Zbl 0706.00007) and \textit{P. Erdös}, A tribute to Paul Erdös, 467-478 (1990; Zbl 0709.11003)]. In this note the author proves an interesting asymptotic version of this Erdös conjecture for the special case of sets which lie in a parallel half-strip.
reviewed by: Erhard Quaisser
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 896020
zbMATH Keywords: minimal diameter of sets
zbMATH Keywords: Erdös-diameter of sets
zbMATH Keywords: unsolved problems
zbMATH Keywords: Erdös conjecture
author: Peter Brass
MaRDI profile type: Publication
cites work: Q3358747
cites work: The maximum number of second smallest distances in finite planar sets
cites work: The number of different distances determined by a set of points in the Euclidean plane
cites work: Unsolved problems in geometry
cites work: Q3684740
cites work: Q3491635
cites work: Q5749340
cites work: Q3946727
cites work: Q4860364
full work available at URL: 0012-365x(95)00208-e
OpenAlex ID: W2081643856
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description: scientific article; zbMATH DE number 896020