The unit distance graph on has edges between those pairs of points at Euclidean distance . The chromatic number of this graph lies between (by exhibiting a small subgraph on vertices with chromatic number ) and (by an explicit colouring based on a hexagonal tiling of the plane). Aubrey de Grey has just posted a …

# Tag: open-problem

## Random Structures and Algorithms 2017

## The Namer-Claimer game

Consider the following game played on the integers from to . In each round Namer names a forbidden distance , then Claimer claims a subset of that does not contain any two integers at distance . After finitely many rounds, Claimer will have claimed sets that cover the whole of , at which point the …