English

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 GG to traverse all mm edges of GG, and return to its starting point, is at most 2m22m^2; if each edge must be traversed in both directions, the bound is 3m23m^2. 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 mm.

Keywords

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}
}
R2 v1 2026-06-21T19:12:46.802Z