Problem 911

Erdős Problem #911: declared status 'open'. Formalized: no. Let $\hat{R}(G)$ denote the size Ramsey number, the minimal number of edges $m$ such that there is a graph $H$ with $m$ edges that is Ramsey for $G$. Is there a function $f$ such that $f(x)/x\to \infty$ as $x\to \infty$ such that, for all large $C$, if $G$ is a graph with $n$ vertices and $e\geq Cn$ edges then$$\hat{R}(G) > f(C) e?$$ Prize: no. Tags: graph theory, ramsey theory.