For a hypergraph $H$, we denote by $\nu(H)$ the maximum size of a set of disjoint edges in $H$. The parameter $\tau(H)$ is defined to be the minimum size of cover in $H$, that is, a set $C$ of vertices that intersects every edge of $H$. We discuss the class of combinatorial problems (some notoriously old and difficult) that seeks to establish upper bounds for $\tau(H)$ in terms of $\nu(H)$ for certain classes of hypergraphs $H$.
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