Let $g (n)$ be the maximum number of different sizes of cliques that can occur in a graph on $n$ vertices. Estimate $g (n)$ - in particular, is it true that $g (n) = n - lo g_{2} n - lo g_{} (n) + O (1),$ where $lo g_{} (n)$ is the number of iterated logarithms such that $lo g \dots lo g n < 1$ .

Worked, still open.

graph theory · solved · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

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

This is **open in general** for a *fixed, specified* irrational (\alpha>1).

solved