论文标题
分分平衡的超图和彩虹KKM定理
Fractionally balanced hypergraphs and rainbow KKM theorems
论文作者
论文摘要
D-Partite HyperGraph被称为 *分数平衡 *如果存在非阴性，而不是相同的零，则在其边缘集合的函数中，每个顶点侧具有恒定度。使用霍尔定理的拓扑版本，我们证明了此类超图的匹配数量的下限。这些边界生成了简单产品的KKM定理的彩虹版本，而这些范围又用于获得多蛋糕划分的一些结果，以及在D互换家族的彩虹匹配方面。
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.
