@article{ECP1022,
author = {Johan Jonasson and Oded Schramm},
title = {On the Cover Time of Planar Graphs},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {5},
year = {2000},
keywords = {effective resistance, commute time, hitting time, difference time,circle packing, triangulation},
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 $\bigl(1+o(1)\bigr)n\log n$ and at most $\bigl(1+o(1)\bigr)\frac{4}{27}n^3$. 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.},
pages = {no. 10, 85-90},
issn = {1083-589X},
doi = {10.1214/ECP.v5-1022},
url = {http://ecp.ejpecp.org/article/view/1022}}