Fractionally Balanced Hypergraphs and Rainbow KKM Theorems
نویسندگان
چکیده
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 topological version of Hall’s theorem we prove lower bounds the matching number such hypergraphs. These yield rainbow versions KKM for products simplices, which turn are used to obtain some results multiple-cake division, and matchings families d-intervals.
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2022
ISSN: ['0209-9683', '1439-6912']
DOI: https://doi.org/10.1007/s00493-021-4808-y