51. Well-mixing vertices and almost expanders
- Author
-
Chakraborti, Debsoumya, Kim, Jaehoon, Kim, Jinha, Kim, Minki, and Liu, Hong
- Subjects
Mathematics - Combinatorics ,Computer Science - Discrete Mathematics - 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)., Comment: accepted in PAMS
- Published
- 2021
- Full Text
- View/download PDF