We discuss several results related to the time taken for a random walk
to visit all vertices of a graph, the cover time. We first discuss
this in relation to two classical models of random graphs
viz. G(n,p) and random r-regular graphs. We give quite precise
estimates for the cover time. We then consider a random walk on a
rather simplified model of a "web-graph". We give a quite precise
estimate of the cover-time and then estimate the proportion of
vertices visited by a "spider" which walks as the graph is
growing. Finally, we consider the problem of determining the
strong-connectivity or otherwise of a randomly perturbed digraph.

Lecture #10822

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