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Numerical evidence against a conjecture on the cover time of planar graphs
Numerical evidence the cover times of planar graphs Statistical Mechanics
2011/7/28
Abstract: We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time $\tau(G_{N})$ of a planar graph $G_{N}$ o...
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small.
More precisely, for every D and C, there exists a=a(D,C)>0 such t...