Let $G$ be a graph such that $R(G,T_n)\ll n$ for any tree $T_n$ on $n$ vertices and $R(G,K_n)\ll n^2$. Is it true that, for any $H$ with $m$ edges and no isolated vertices,$$R(G,H)\ll m?$$

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

What you’re asking is exactly whether such a graph $G$ must be **Ramsey size-linear**: i.e., whether there is a constant (C_G) so that for every graph $H$ with no isolated vertices, [ R(G,H)\le C_G, e(H). ] This formulation (and the broader programme) was introduced by Erdős–Faudree–Rousseau–Schelp. ([Cambridge Univers…

llm-hunter · codex 5.2 extra high, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (codex 5.2 extra high, gpt pro 5.2); unverified.