System of distinct representatives

System of distinct representatives --- система различных представителей.

Given a hypergraph [math]\displaystyle{ {\mathcal H} }[/math], a system of distinct representatives is a one-to-one mapping [math]\displaystyle{ \varrho: \; E({\mathcal H}) \rightarrow V({\mathcal H}) }[/math] such that [math]\displaystyle{ \varrho(E) \in E }[/math] for each [math]\displaystyle{ E \in E({\mathcal H}) }[/math]. If no confusion can arise, we also call the range [math]\displaystyle{ \varrho(E({\mathcal H})) }[/math] a system of distinct representatives.