Let $R(k)$ denote the smallest $R$ such that for any $k$-colouring of the edges of the complete graph $K_R$ some triangle is monochromatic. By Ramsey’s theorem, $R(k)$ exists for all $k$. It is shown that if an edge $e$ is removed, the remaining graph $K_R-e$ has a $k$-colouring with no triangle monochromatic. The author of the paper attributes this result to Herbert Taylor.
Reviewer: Konrad Swanepoel (Chemnitz)