A hypergraph is called '''totally balanced''' iffif every cycle ''C'' in ''H'' of length at least 3 (not necessarily odd-length) has an edge containing at least three vertices of ''C''.<ref name=":2">{{Cite journal|last=Lehel|first=Jenö|date=1985-11-01|title=A characterization of totally balanced hypergraphs|url=http://www.sciencedirect.com/science/article/pii/0012365X85901566|journal=Discrete Mathematics|language=en|volume=57|issue=1|pages=59–65|doi=10.1016/0012-365X(85)90156-6|issn=0012-365X}}</ref>
Lehel proved that a hypergraph H is totally balanced iff every subhypergraph of H is a tree-hypergraph.<ref name=":2" />
