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2000 On the Cover Time of Planar Graphs
Johan Jonasson, Oded Schramm
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Electron. Commun. Probab. 5: 85-90 (2000). DOI: 10.1214/ECP.v5-1022

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.

Citation

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Johan Jonasson. Oded Schramm. "On the Cover Time of Planar Graphs." Electron. Commun. Probab. 5 85 - 90, 2000. https://doi.org/10.1214/ECP.v5-1022

Information

Accepted: 5 May 2000; Published: 2000
First available in Project Euclid: 2 March 2016

zbMATH: 0949.60083
MathSciNet: MR1781842
Digital Object Identifier: 10.1214/ECP.v5-1022

Subjects:
Primary: 60J10
Secondary: 52C15

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