On the cover time of dense graphs

10/10/2018

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by   Colin Cooper, et al.

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We consider arbitrary graphs G with n vertices and minimum degree at least δ n where δ>0 is constant. If the conductance of G is sufficiently large then we obtain an asymptotic expression for the cover time C_G of G as the solution to an explicit transcendental equation. Failing this, if the mixing time of a random walk on G 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 C_G.