Kalai's tight hypertree conjecture

Let $\mathcal H$ be an $r$-uniform hypergraph with $n$ vertices, and let a tight $r$-uniform hypertree with $k$ edges be the target hypergraph.

Kalai's conjecture. If

$$e(\mathcal H)\geq \frac{k-1}{r}\binom{n}{r-1},$$

then $\mathcal H$ contains a copy of every tight $r$-uniform hypertree with $k$ edges.

This is a hypergraph generalization of the Erdős–Sós conjecture. The source presents it as an open problem among generalizations to hypergraphs and directed graphs.