Totally balanced hypergraph

Totally balanced hypergraph --- тотально сбалансированный гиперграф.

A hypergraph is totally balanced if every cycle of length greater than two has an edge containing at least three vertices of the cycle. It is known that a hypergraph [math]\displaystyle{ {\mathcal H} }[/math] is totally balanced if and only if every subhypergraph of [math]\displaystyle{ {\mathcal H} }[/math] is a hypertree. See also Balanced hypergraph.