On the cover time of random walks on graphs

Jeff D. Kahn; Nathan Linial; Noam Nisan; Michael E. Saks

doi:10.1007/BF01048274

On the cover time of random walks on graphs

Jeff D. Kahn^*, Nathan Linial, Noam Nisan, Michael E. Saks

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

This article deals with random walks on arbitrary graphs. We consider the cover time of finite graphs. That is, we study the expected time needed for a random walk on a finite graph to visit every vertex at least once. We establish an upper bound of O(n²) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of Ω(n log n) for the expected cover time for trees. We present examples showing all our bounds to be tight.

Original language	English
Pages (from-to)	121-128
Number of pages	8
Journal	Journal of Theoretical Probability
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/BF01048274
State	Published - Jan 1989

Keywords

Random walks
cover times
graphs
infinite graphs
trees

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10.1007/BF01048274

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On the cover time of random walks on graphs

Abstract

Keywords

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