Let $R(k,l)$ be the Ramsey number, so the minimal $n$ such that every graph on at least $n$ vertices contains either a $K_k$ or an independent set on $l$ vertices.Prove, for fixed $k\ge 3$, that$$\underset{l\to \infty }{\lim }\frac{R(k,l+1)}{R(k,l)}=1.$$

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

Fix an integer (k\ge 3), and write [ r_l:=R(k,l). ] We will show (r_{l+1}/r_l\to 1).

llm-hunter · gpt pro 5.2 · unverified

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