论婚姻问题的泛化概括

作者：Jonathan Lenchner

摘要：我们将Hall著名的婚姻定理的婚姻问题概括为我们称之为对称婚姻问题，这个问题可以被认为是最大加权二元匹配的一个特例。 我们证明了对称婚姻问题的解决方案，当且仅当霍尔条件的变化适用于每个二分法时。 我们证明了这个结果的有限和无限版本，并提供了应用程序。

原文标题：On a Generalization of the Marriage Problem

原文摘要：We present a generalization of the marriage problem underlying Hall's famous Marriage Theorem to what we call the Symmetric Marriage Problem, a problem that can be thought of as a special case of Maximal Weighted Bipartite Matching. We show that there is a solution to the Symmetric Marriage Problem if and only if a variation on Hall's Condition holds on each of the bipartitions. We prove both finite and infinite versions of this result and provide applications.

地址：https://arxiv.org/abs/1907.05870