Random Walks with Look-Ahead in Scale-Free Random Graphs

If $m\geq2$ is constant and $0\leq r\leq\varepsilon\log\log n$ for a small positive constant $\varepsilon$, then whp a random walk with look-ahead $r$ on a scale-free graph $G=G_{(m,n)}$ has cover time $C_G(r)\sim(2/(m^{r-1}(m-1)))\;n\log n$.

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