Restriction of a hypergraph

Restriction of a hypergraph --- сужение гиперграфа.

The restriction of a hypergraph [math]\displaystyle{ {\mathcal H} }[/math] onto [math]\displaystyle{ X \subset V({\mathcal H}) }[/math] is the hypergraph [math]\displaystyle{ {\mathcal H}_{X} }[/math] on the set [math]\displaystyle{ X }[/math], for which [math]\displaystyle{ E({\mathcal H}_{X}) }[/math] is the collection of sets [math]\displaystyle{ E \cap X }[/math], [math]\displaystyle{ E \in E({\mathcal H}) }[/math]. If [math]\displaystyle{ X = V({\mathcal H}) - Y }[/math], then we adopt the notation [math]\displaystyle{ {\mathcal H}_{X} = {\mathcal H} \setminus Y }[/math] and [math]\displaystyle{ {\mathcal H}_{X} = {\mathcal H} - y }[/math], if [math]\displaystyle{ Y = \{y\} }[/math].