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Balance does not imply bipartiteness. Let ''H'' be the hypergraph:<ref>{{Cite web|title=coloring - Which generalization of bipartite graphs is stronger?|url=https://math.stackexchange.com/questions/3728221/which-generalization-of-bipartite-graphs-is-stronger|access-date=2020-06-27|website=Mathematics Stack Exchange}}</ref><blockquote>{ {1,2} , {3,4} , {1,2,3,4} }</blockquote>it is 2-colorable and remains 2-colorable upon removing any number of vertices from it. However, It is not bipartite, since to have exactly one green vertex in each of the first two hyperedges, we must have two green vertices in the last hyperedge.
== Totally balanced hypergraphs ==
A hypergraph is called '''totally balanced''' iff every cycle ''C'' in ''H'' of length at least 3 has an edge containing at least three vertices of ''C''.<ref>{{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>
== References ==
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