Let $f_{k} (n)$ be the maximum possible chromatic number of a graph with $n$ vertices which contains no $K_{k}$ .Is it true that, for $k \geq 4$ , $f_{k} (n) ≫ \frac{n ^{1 - \frac{1}{k - 1}}}{( lo g n ) ^{c_{k}}}$ for some constant $c_{k} > 0$ ?

Worked, still open.

graph theory · open · possible · formalized (Lean) · 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

There’s a very tight connection here to **off‑diagonal Ramsey numbers**.

llm-hunter · gpt pro 5.2 · unverified

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

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