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New Bounds for Edge-Cover by Random Walk
We show that the expected time for a random walk on a (multi-)graph to
traverse all edges of , and return to its starting point, is at most
; if each edge must be traversed in both directions, the bound is .
Both bounds are tight and may be applied to graphs with arbitrary edge lengths,
with implications for Brownian motion on a finite or infinite network of total
edge-length
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