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New Bounds for Edge-Cover by Random Walk

Published online by Cambridge University Press:  11 March 2014

AGELOS GEORGAKOPOULOS  and
PETER WINKLER
AGELOS GEORGAKOPOULOS
Affiliation:
Mathematics Institute, University of Warwick, CV4 7AL, UK (e-mail: a.georgakopoulos@warwick.ac.uk)
PETER WINKLER
Affiliation:
Department of Mathematics, Dartmouth, Hanover, NH 03755-3551, USA (e-mail: peter.winkler@dartmouth.edu)
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Abstract

We show that the expected time for a random walk on a (multi-)graph G to traverse all m edges of G, 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.

Keywords

Primary 05C81Secondary 60J65

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 4 , July 2014 , pp. 571 - 584
Copyright
Copyright © Cambridge University Press 2014 

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