Speaker: Lu Hongliang, Professor, doctoral supervisor at the School of Mathematics and Statistics, Xi’an Jiaotong University

Date: November 11, 2022

Time: 14:00-15:00

Location: Zoom

Sponsor: School of Mathematics, Shandong University

Abstract:

Let k and n be two integers, with k≥4, where n≡0 (mod 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 Rödl, Rucin ́ski, and Szemerédi 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 Rödl, Rucin ́ski, and Szemerédi. This is joint work with Wang Yang and Yu Xingxing.

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https://www.view.sdu.edu.cn/info/1020/171920.htm