Speaker: Liu Hong, Leader of ECOPRO

Date: February 14, 2023

Time: 10:30-11:30

Location: 924 lecture hall, Block B, Zhixin Building, Central Campus

Sponsor: School of Mathematics, Shandong University

Abstract:

We study regular graphs in which the random walks starting from a positive fraction of vertices have small mixing time. We prove that any such graph is virtually an expander and has no small separator. This answers a question of Pak [SODA, 2002]. As a corollary, it shows that sparse (constant degree) regular graphs with many well-mixing vertices have a long cycle, improving a result of Pak. Furthermore, such cycle can be found in polynomial time. Secondly, we show that if the random walks from a positive fraction of vertices are well-mixing, then the random walks from almost all vertices are well-mixing (with a slightly worse mixing time).

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/175413.htm