Connected hypergraph

Connected hypergraph --- связный гиперграф.

A hypergraph such that it is not representable as [math]\displaystyle{ {\mathcal H}_{1} \cup {\mathcal H}_{2} }[/math], where [math]\displaystyle{ {\mathcal H}_{1}, {\mathcal H}_{2} }[/math] are vertex-disjoint non-empty hypergraphs is called connected. Note that if [math]\displaystyle{ \emptyset \in E({\mathcal H}) }[/math], [math]\displaystyle{ {\mathcal H} }[/math] is not connected.