发表机构
Beijing Institute of Technology; Xi’an Jiaotong University（北京理工大学; 西安交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文确定了$k\ge5$时平衡$k$部$k$均匀超图中完美匹配的最小顶点度阈值，推广了Lo-Markström和Lu-Wang-Yuan的结果，并利用概率尾部刚性定理处理非封闭情形。
AI 中文摘要
一个平衡的$k$部$k$图是一个$k$均匀超图，其顶点集被划分为大小相同的$k$个类，且每条边恰好从每个类中选取一个顶点。Lo和Markström（2014）确定了当$k=3$时完美匹配的最小顶点度阈值，而Lu、Wang和Yuan最近确定了当$k=4$时的阈值。我们证明了对于每个固定的$k\ge5$以及所有足够大的类大小，相应的精确结果。封闭情形由Lu、Wang和Yuan的一般定理得出。对于非封闭情形，我们将他们的稳定性结果从3部设置推广到任意部均匀性，使用Cao、Liu和Zhang的概率尾部刚性定理，从而取代了早期的加权引理。
英文摘要
A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph whose vertex set is partitioned into $k$ classes of the same size and whose edges meet every class in exactly one vertex. Lo and Markström (2014) determined the minimum vertex-degree threshold for perfect matchings when $k=3$, and Lu, Wang and Yuan recently determined it when $k=4$. We prove the corresponding exact result for every fixed $k\ge5$ and all sufficiently large class sizes. The close case follows from the general theorem of Lu, Wang and Yuan. For the non-closed case, we extend their stability result from the 3-partite setting to arbitrary partite uniformity, using the probability-tail rigidity theorem of Cao, Liu and Zhang, thereby replacing the earlier weighted lemma.
Comments12 pages
