On four-colourings of the rational four-space

Joseph Zaks

doi:10.1007/BF01836448

On four-colourings of the rational four-space

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let Q⁴ denote the graph, obtained from the rational points of the 4-space, by connecting two points iff their Euclidean distance is one. It has been known that its chromatic number is 4. We settle a problem of P. Johnson, showing that in every four-colouring of this graph, every colour class is every-where dense.

Original language	English
Pages (from-to)	259-266
Number of pages	8
Journal	Aequationes Mathematicae
Volume	37
Issue number	2-3
DOIs	https://doi.org/10.1007/BF01836448
State	Published - Jun 1989

Keywords

AMS (1980) subject classification: Primary 05C15, Secondary 51K05, 52A37

ASJC Scopus subject areas

General Mathematics
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/BF01836448

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AB - Let Q4 denote the graph, obtained from the rational points of the 4-space, by connecting two points iff their Euclidean distance is one. It has been known that its chromatic number is 4. We settle a problem of P. Johnson, showing that in every four-colouring of this graph, every colour class is every-where dense.

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JO - Aequationes Mathematicae

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IS - 2-3

ER -

On four-colourings of the rational four-space

Abstract

Keywords

ASJC Scopus subject areas

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