English

Coloring the distance graph in three dimensions

Logic 2021-03-19 v2

Abstract

Let Gn be the graph on n-dimensional Euclidean space connecting points of rational Euclidean distance. It is consistent relative to an inaccessible cardinal that ZF+DC holds and G3 has countable chromatic number, yet G4 has uncountable chromatic number.

Keywords

Cite

@article{arxiv.2103.02757,
  title  = {Coloring the distance graph in three dimensions},
  author = {Jindrich Zapletal},
  journal= {arXiv preprint arXiv:2103.02757},
  year   = {2021}
}
R2 v1 2026-06-23T23:44:06.861Z