Let $r \geq 3$ . There exists $c_{r} > r^{- r}$ such that, for any $ϵ > 0$ , if $n$ is sufficiently large, the following holds.Any $r$ -uniform hypergraph on $n$ vertices with at least $(1 + ϵ) (n / r)^{r}$ many edges contains a subgraph on $m$ vertices with at least $c_{r} m^{r}$ edges, where $m = m (n) \to \infty$ as $n \to \infty$ .

Worked, still open.

hypergraphs · open · 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

What you wrote is *exactly* the “boundary case” of Erdős’s **jump problem** for $r$-uniform hypergraphs.

llm-hunter · gpt pro 5.2 · unverified

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

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