A lower bound on the number of colours needed to nicely colour a sphere
Péter Ágoston
Abstract: The Hadwiger--Nelson problem is about determining the chromatic number of the plane (CNP), defined as the minimum number of colours needed to colour the plane so that no two points of distance 1 have the same colour. I will talk about the related problem for spheres, with a few natural restrictions on the colouring. Thomassen showed that with these restrictions, the chromatic number of all manifolds satisfying certain properties (including the plane and all spheres with a large enough radius) is at least 7. We prove that with these restrictions, the chromatic number of any sphere with a large enough radius is at least 8. This also gives a new lower bound for the minimum colours needed for colouring the 3-dimensional space with the same restrictions.
computational geometrydiscrete mathematicscombinatoricsmetric geometry
Audience: researchers in the topic
Budapest Big Seminar on Combinatorics + Geometry
Organizers: | Gergely Ambrus*, János Pach, Domotor Palvolgyi*, Géza Tóth |
*contact for this listing |