Balanced hypergraph: Difference between revisions

Revision as of 02:03, 30 January 2023

Revision as of 03:02, 23 February 2023

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The balanced hypergraphs are exactly the hypergraphs H such that every ''partial subhypergraph'' of ''H'' has the Konig property (i.e., H has the Konig property even upon deleting any number of hyperedges and vertices).

If every ''partial'' hypergraph of H has the Konig property (i.e., H has the Konig property even upon deleting any number of hyperedges - but not vertices), then H is called a '''normal hypergraph'''.<ref name=":02">{{Cite journal|last1=Beckenbach|first1=Isabel|last2=Borndörfer|first2=Ralf|date=2018-10-01|title=Hall's and Kőnig's theorem in graphs and hypergraphs|url=http://www.sciencedirect.com/science/article/pii/S0012365X18301845|journal=Discrete Mathematics|language=en|volume=341|issue=10|pages=2753–2761|doi=10.1016/j.disc.2018.06.013|s2cid=52067804 |issn=0012-365X|doi-access=free}}</ref>

Thus, totally-balanced implies balanced, which implies normal.