DIAGONAL RAMSEY VIA EFFECTIVE QUASIRANDOMNESS

摘要

We improve the upper bound for diagonal Ramsey numbers to R(k + 1, k + 1) = 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 opti-mality represents a natural barrier to improvement.