| On the cover time of planar graphs (2000) | |||||||||
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.. Comment: To appear in Electronic Communications in Probability | |||||||||
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