On the cover time of planar graphs
Probability
2008-11-26 v3
Abstract
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time on any n-vertex, connected graph is at least (1+o(1)) n log(n) and at most (1+o(1))(4/27)n^3. This paper proves that for bounded-degree planar graphs the cover time is at least c n(log n)^2, and at most 6n^2, where c is a positive constant depending only on the maximal degree of the graph. The lower bound is established via use of circle packings.
Keywords
Cite
@article{arxiv.math/0002034,
title = {On the cover time of planar graphs},
author = {Johan Jonasson and Oded Schramm},
journal= {arXiv preprint arXiv:math/0002034},
year = {2008}
}
Comments
To appear in Electronic Communications in Probability