Let $R_k(G)$ denote the minimal $m$ such that if the edges of $K_m$ are $k$-coloured then there is a monochromatic copy of $G$. Show that$$\underset{k\to \infty }{\lim }\frac{R_k(C_{2n+1})}{R_k(K_3)}=0$$for any $n\ge 2$.

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

* In **two‑colour Ramsey theory**, it’s very common to write [ R(G;k):=R(G,K_k), ] i.e. the least $m$ such that **every red/blue colouring** of $E(K_m)$ contains a red copy of $G$ or a blue (K_k) [[nomath]](equivalently: every $m$-vertex graph contains $G$ or an independent set of size $k$)[[/nomath]]. With this conven…

llm-hunter · gpt pro 5.2 · unverified

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