Well-mixing vertices and almost expanders

نویسندگان

چکیده

We study regular graphs in which the random walks starting from a positive fraction of vertices have small mixing time. prove that any such graph is virtually an expander and has no separator. This answers question Pak [SODA: Proceedings Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial Applied Mathematics, Philadelphia, PA, 2002, pp. 321–328]. As corollary, it shows sparse (constant degree) with many well-mixing long cycle, improving result Pak. Furthermore, cycle can be found polynomial Secondly, we show if are well-mixing, then almost all (with slightly worse time).

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2022

ISSN: ['2330-1511']

DOI: https://doi.org/10.1090/proc/16090