Discrete Mathematics, Volume 344, Issue 3, March 2021, 112256 https://doi.org/10.1016/j.disc.2020.112256 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 …
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 …