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On the cover time of dense graphs
We consider arbitrary graphs with vertices and minimum degree at
least where is constant. If the conductance of is
sufficiently large then we obtain an asymptotic expression for the cover time
of as the solution to an explicit transcendental equation. Failing
this, if the mixing time of a random walk on is of a lesser magnitude than
the cover time, then we can obtain an asymptotic deterministic estimate via a
decomposition into a bounded number of dense sub-graphs with high conductance.
Failing this we give a deterministic asymptotic (2+o(1))-approximation of