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 $e\ge Cn$ edges then$$\hat{R}(G)>f(C)e?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This exact question is (as far as I can tell from the current literature) **open**. It appears as **Erdős problem #911** on the Erdős Problems website, with the same formulation in terms of graphs with (e(G)\ge C,v(G)) and asking for a lower bound (\hat R(G)\ge f(C),e(G)) with (f(C)/C\to\infty). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.