New Bounds for Edge-Cover by Random Walk
Combinatorics
2019-02-20 v1 Discrete Mathematics
Abstract
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 .
Cite
@article{arxiv.1109.6619,
title = {New Bounds for Edge-Cover by Random Walk},
author = {Agelos Georgakopoulos and Peter Winkler},
journal= {arXiv preprint arXiv:1109.6619},
year = {2019}
}