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.
- AMS (1980) subject classification: Primary 05C15, Secondary 51K05, 52A37
ASJC Scopus subject areas
- Mathematics (all)
- Discrete Mathematics and Combinatorics
- Applied Mathematics