The cover time of the giant component of a random graph

We study the cover time of a random walk on the largest component of the random graph Gn,p. We determine its value up to a factor 1 + o(1) whenever np = c > 1, c = O(lnn). In particular we show that the cover time is not monotone for c = Θ(lnn). We also determine the cover time of the k-cores, k ≥ 2.

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