报告题目 (Title)：Co-degree threshold for rainbow perfect matchings in uniform hypergraphs（关于一致超图上有彩色完美匹配的余度阈值问题）

报告人 (Speaker)：鲁红亮 教授（西安交通大学）

报告时间 (Time)：2023年9月21日(周四) 14:30

报告地点 (Place)：校本部D204、腾讯会议号546 972 901

邀请人(Inviter)：杨倩倩

主办部门：理学院数学系

报告摘要： Let k and n be two integers, with k\geq 3, n\equiv 0\pmod k, and n sufficiently large. We determine the (k-1)-degree threshold for the existence of a rainbow perfect matchings in n-vertex k-uniform hypergraph. This implies the result of R\"odl, Ruci\'nski, and Szemer\'edi on the (k-1)-degree threshold for the existence of perfect matchings in n-vertex k-uniform hypergraphs. In our proof, we identify the extremal configurations of closeness, and consider whether or not the hypergraph is close to the extremal configuration. In addition, we also develop a novel absorbing device and generalize the absorbing lemma of R\"odl, Ruci\'nski, and Szemer\'edi. This is joint work with Yan Wang and Xingxing Yu.