HN submission. Found in a submission link or body. Submitters do not count as commenters in the main ranking; a submission is not an endorsement.
Abstract
We improve the upper bound on the Ramsey number $R(5,5)$ from $R(5,5) \le 49$ to $R(5,5) \le 48$. We also complete the catalogue of extremal graphs for $R(4,5)$.