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Well-mixing vertices and almost expanders
- Publication Year :
- 2021
-
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).<br />Comment: accepted in PAMS
- Subjects :
- Mathematics - Combinatorics
Computer Science - Discrete Mathematics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2108.12864
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1090/proc/16090