The Namer-Claimer game, part 2

arXiv I’ve previously written about the Namer-Claimer game.  I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound.  The upper bound makes use of randomness, but in a very controlled way.  Analysing a truly random strategy still seems like it will be very …

Chromatic number of the plane

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 …