A $6$-chromatic two-distance graph in the plane

Abstract

We prove that if one colors each point of the Euclidean plane with one of five colors, then there exist two points of the same color that are either distance $1$ or distance $2$ apart.

arXiv comment7 pages, 1 figure

References in corpus (2)

• Computing Small Unit-Distance Graphs with Chromatic Number 5
• The Hadwiger-Nelson problem with two forbidden distances

Cited by in corpus (1)

• A small 6-chromatic two-distance graph in the plane