On lower bounds for the chromatic number of sphere
type: Item
instance of: scholarly article
title: On lower bounds for the chromatic number of sphere
zbMATH Open document ID: 1330.52021
DOI: 10.1134/S1064562415040298
published in: Doklady Mathematics
publication date: 2015-11-12T00:00:00Z
review text: The last lower bound for the chromatic number of the unit distance graph, whose vertex set is a sphere of radius \(r\) in the \(n\)-dimensional Euclidean space is due to Raigorodskii, the second author of the paper under review. He showed that for any fixed \(r>\frac12\) the chromatic number grows exponentially with \(n\). His lower bound, however, did not depend on \(r\) for \(\frac{1}{\sqrt{2}}<r\). This paper provides improved lower bounds that do depend on \(r\) if \(\frac{1}{\sqrt{2}}<r<\frac{1}{\root{4}\of{2}}\).
reviewed by: László A. Székely
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 6507789
zbMATH Keywords: unit distance graph
zbMATH Keywords: chromatic number
author: Olga A. Kostina
author: Andrei M. Raigorodskii
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6507789