On Some Small Classical Ramsey Numbers

Abstract

This note is a report on a computer investigation of some small classical Ramsey numbers. We establish new lower bounds for the classical Ramsey numbers $R(3,11)$ and $R(4,8)$. In the first case, the bound is improved from $46$ (a record that had stood for 46 years) to $47$; and in the second case the bound is improved from $57$ to $58$.