arXiv:2005.09251math.CO
Diagonal Ramsey via effective quasirandomness
Abstract
We improve the upper bound for diagonal Ramsey numbers to \[R(k+1,k+1)\le\exp(-c(\log k)^2)\binom{2k}{k}\] for $k\ge 3$. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal "effective quasirandomness" results about convergence of graphs. This optimality represents a natural barrier to improvement.
https://arxiv.org/pdf/2005.09251.pdf
hankchinaskiView on HNParent context
For the Ramsay paper in particular (with a short easy to read introduction): https://arxiv.org/pdf/2005.09251.pdf
thomasahleView on HNParent context