On the cover time of random walks on graphs
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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 ofO(n2) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of Ω(n logn) for the expected cover time for trees. We present examples showing all our bounds to be tight.
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