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تسجيل مستخدم جديدFractionally balanced hypergraphs and rainbow KKM theorems
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A $d$-partite hypergraph is called fractionally balanced if there exists a non-negative function on its edge set that has constant degrees in each vertex side. Using a topological version of Halls theorem we prove lower bounds on the matching number of such hypergraphs. These, in turn, yield results on mulitple-cake division problems and rainbow matchings in families of $d$-intervals.
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