The chromatic number of the plane is at least 5

By A. D. Grey. 2018

134 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/280e80bd566ddd60234bb4f7a248cfb9db563d29