OPEN

Show that if $G$ has $\binom{n}{2}$ edges then
\[R(G) \leq R(n).\]
More generally, if $G$ has $\binom{n}{2}+t$ edges with $t\leq n$ then
\[R(G)\leq R(H)\]
where $H$ is the graph formed by connected a new vertex to $t$ of the vertices of $K_n$.

In other words, are cliques extremal for Ramsey numbers. Asked by Erdős and Graham.

This is true, and was proved by Sudakov [Su11]. The analogous question for $\geq 3$ colours is still open.