Fractionally Balanced Hypergraphs and Rainbow KKM Theorems

Ron Aharoni, Eli Berger, Joseph Briggs, Erel Segal-Halevi, Shira Zerbib

Research output: Contribution to journalArticlepeer-review


A d-partite hypergraph is called fractionally balanced if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall’s theorem we prove lower bounds on the matching number of such hypergraphs. These bounds yield rainbow versions of the KKM theorem for products of simplices, which in turn are used to obtain some results on multiple-cake division, and on rainbow matchings in families of d-intervals.

Original languageEnglish
Pages (from-to)913-951
Number of pages39
Issue number6
StatePublished - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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