K-Cover of a (hyper)graph

[math]\displaystyle{ k }[/math]-Cover of a (hyper)graph --- [math]\displaystyle{ k }[/math]-покрытие (вершинное) графа (гиперграфа).

This is a collection of points such that each edge contains at least [math]\displaystyle{ k }[/math] of them. 1-cover is simply a vertex (point) cover. A [math]\displaystyle{ k }[/math]-cover can also be regarded as a mapping [math]\displaystyle{ t: \; V(G) \rightarrow \{0, 1, \ldots\} }[/math] such that [math]\displaystyle{ \sum_{x \in E} t(x) \geq k }[/math] for each edge [math]\displaystyle{ E }[/math].