On four-colourings of the rational four-space
type: Item
instance of: scholarly article
title: On four-colourings of the rational four-space
zbMATH Open document ID: 0705.05033
DOI: 10.1007/BF01836448
author: Joseph Zaks
published in: Aequationes Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137304
review text: Let \(Q^ p\) denote the collection of all the rational points of the p- space \(E^ p\), and let \(G(Q^ p)\) denote the graph, obtained by taking \(Q^ p\) as the vertex set, and connecting 2 points iff they are at a distance 1 (the usual Euclidean distance). There is shown that in every 4-colouring of \(G(Q^ p)\) every colour is everywhere dense. The chromatic number of \(G(Q^ 6)\), \(G(Q^ 7)\) and \(G(Q^ 8)\) is at least 6, 8 and 9, respectively.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 51K05
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 4156468
zbMATH Keywords: chromatic number
reviewed by: Jozef Fiamčík
MaRDI profile type: Publication
cites work: Intersection theorems with geometric consequences
cites work: Distances realized by sets covering the plane
description: scientific article; zbMATH DE number 4156468