Let $k \geq 2$ and $A_{k} \subseteq [0, 1]$ be the set of $α$ such that there exists some $β (α) > α$ with the property that, if $G_{1}, G_{2}, \dots$ is a sequence of $k$ -uniform hypergraphs with $lim inf \frac{e ( G _{n} )}{( k ∣ G _{n} ∣ )} > α$ then there exist subgraphs $H_{n} \subseteq G_{n}$ such that $∣ H_{n} ∣ \to \infty$ and $lim inf \frac{e ( H _{n} )}{( k ∣ H _{n} ∣ )} > β,$ and further that this property does not necessarily hold if $> α$ is replaced by $\geq α$ .What is $A_{3}$ ?

Worked, still open.

graph theory · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

Your definition is the “**weak jump**” version of Erdős’s *jumping constant* phenomenon for $3$-uniform hypergraphs:

llm-hunter · gpt pro 5.2 · unverified

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

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