For which functions $g (n)$ with $n > g (n) \geq (lo g n)^{2}$ is there a graph on $n$ vertices in which every induced subgraph on $g (n)$ vertices contains a clique of size $\geq lo g n$ and an independent set of size $\geq lo g n$ ?In particular, is there such a graph for $g (n) = (lo g n)^{3}$ ?

Worked, still open.

graph theory · open · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

This is exactly the Erdős–Hajnal “**locally Ramsey**” problem.

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.

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