Abstract

We present two novel six-colourings of the Euclidean plane that avoid monochromatic pairs of points at unit distance in five colours and monochromatic pairs at another specified distance d in the sixth colour. Such colourings have previously been known to exist for 0.41 < sqrt(2)- 1 <= d <= 1 / sqrt(5) < 0.45. Our results significantly expand that range to 0.354 <= d <= 0.657, the first improvement in 30 years. Notably, the constructions underlying this were derived by formalising colourings suggested by a custom machine learning approach.

 

This is joint work with Sebastian Pokutta, Konrad Mundiger, and Max Zimmer.

 

Organizer: Shagnik Das (NTU)