On the cover time of random walks on graphs

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


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 languageAmerican English
Pages (from-to)121-128
Number of pages8
JournalJournal of Theoretical Probability
Issue number1
StatePublished - Jan 1989


  • Random walks
  • cover times
  • graphs
  • infinite graphs
  • trees


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