The evolution of the mixing rate of a simple random walk on the giant component of a random graph
Random Structures & Algorithms
Stationary distribution and cover time of random walks on random digraphs
Journal of Combinatorial Theory Series B
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The above paper gives an asymptotically precise estimate of the cover time of the giant component of a sparse random graph. The proof as it stands is not tight enough, and in particular, Eq. (64) is not strong enough to prove (65). The o(1) term in (64) needs to be improved to o(1-(lnn)2) for (65) to follow. The following section, which replaces Section 3.6, amends this oversight. The notation and definitions are from the paper. A further correction is needed. Property P2 claims that the conductance of the giant is whp, Ω(1-lnn). The proof of P2 in the appendix of the paper is not quite complete. A complete proof of Property P2 can be found in [1,2]. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009