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on Erdős #643 · graph theory / hypergraphs

The statement

Let $f(n;t)$ be minimal such that if a $t$ -uniform hypergraph on $n$ vertices contains at least $f(n;t)$ edges then there must be four edges $A,B,C,D$ such that

A\cup B= C\cup D

and

A\cap B=C\cap D=\emptyset.

Estimate $f(n;t)$ - in particular, is it true that for $t\geq 3$

f(n;t)=(1+o(1))\binom{n}{t-1}?

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.