  The Ramsey number $r(G)$ of a graph $G$ is the minimum $N$ such that every
red-blue coloring of the edges of the complete graph on $N$ vertices contains a
monochromatic copy of $G$. Determining or estimating these numbers is one of
the central problems in combinatorics.
  One of the oldest results in Ramsey Theory, proved by Erd\H{o}s and Szekeres
in 1935, asserts that the Ramsey number of the complete graph with $m$ edges is
at most $2^{O(\sqrt{m})}$. Motivated by this estimate Erd\H{o}s conjectured,
more than a quarter century ago, that there is an absolute constant $c$ such
that $r(G) \leq 2^{c\sqrt{m}}$ for any graph $G$ with $m$ edges and no isolated
vertices. In this short note we prove this conjecture.
