The chromatic number of the plane is at least 5

Abstract

We present a family of finite unit-distance graphs in the plane that are not 4-colourable, thereby improving the lower bound of the Hadwiger-Nelson problem. The smallest such graph that we have so far discovered has 1581 vertices.

Cited by in corpus (6)

• Monochromatic Equilateral Triangles in the Unit Distance Graph
• Exact square coloring of subcubic planar graphs
• Chromatic numbers of Cayley graphs of abelian groups: A matrix method
• Constructing 5-chromatic unit distance graphs embedded in the Euclidean plane and two-dimensional spheres
• Monochromatic triangles in the max-norm plane
• Non-local Potts model on random lattice and chromatic number of a plane