New Bounds for Edge-Cover by Random Walk

Abstract

We show that the expected time for a random walk on a (multi-)graphGto traverse allmedges ofG, and return to its starting point, is at most 2m2; if each edge must be traversed in both directions, the bound is 3m2. Both bounds are tight and may be applied to graphs with arbitrary edge lengths. This has interesting implications for Brownian motion on certain metric spaces, including some fractals.