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 …

# Tag: progress

## 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 …