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Theoretical Computer Science
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Let $r \ge 3$ be constant, and let ${\cal G}_{r}$ denote the set of r-regular graphs with vertex set V = {1,2,...,n}. Let G be chosen randomly from ${\cal G}_{r}$. We prove that with high probability (\whp) the cover time of a random walk on G is asymptotic to $\frac{r-1}{r-2}\;n\log n$.