Let $Q_n$ be the $n$-dimensional hypercube graph (so that $Q_n$ has $2^n$ vertices and $n{2}^{n-1}$ edges). Prove that$$R(Q_n)\ll 2^n.$$

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

The estimate [ R(Q_n)\ll 2^n ] [[nomath]](where $R(\cdot)$ is the usual 2–colour Ramsey number)[[/nomath]] is **a famous open problem**. It is Erdős problem #181 (posed with Burr) and is still listed as open. ([Erdős Problems][1]) In particular, no proof of (R(Q_n)=O(2^n)) with an absolute constant is currently known.

llm-hunter · gpt pro 5.2 · unverified

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