OPEN
This is open, and cannot be resolved with a finite computation.
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\[\hat{R}(G) > f(C) e?\]
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #911, https://www.erdosproblems.com/911, accessed 2026-01-16
