On four-colourings of the rational four-space

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)259-266
Number of pages8
JournalAequationes Mathematicae
Volume37
Issue number2-3
DOIs
StatePublished - Jun 1989

Keywords

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

ASJC Scopus subject areas

  • Mathematics (all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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