The packing problem for hypergraphs

Let $H=(V,E)$ be a hypergraph, and let $I(H)$ be its edge ideal. A minor of $H$ is obtained by deleting and contracting vertices. The hypergraph $H$ has the packing property if every minor $h$ is König, that is, if its transversal number equals its matching number, $\tau(h)=\pi(h)$. The packing problem for hypergraphs. The edge ideal satisfies

$$I(H)^{(m)}=I(H)^m$$

for every $m\in\mathbb{N}$ if and only if $H$ has the packing property. This is the combinatorial formulation of the square-free monomial ideal packing problem; its general status is open.