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arXiv · 1810.04772

On the cover time of dense graphs

Colin Cooper·Alan Frieze·Wesley Pegden
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Abstract

We consider arbitrary graphs $G$ with $n$ vertices and minimum degree at least $\delta n$ where $\delta>0$ 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 $C_G$.

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Colin Cooper, Alan Frieze, Wesley Pegden. 2018-10-10. On the cover time of dense graphs. https://arxiv.org/abs/1810.04772

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