On the Cover Time of Planar Graphs
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | On the Cover Time of Planar Graphs |
| 2. | Creator | Author's name, affiliation, country | Johan Jonasson; Chalmers University of Technology |
| 2. | Creator | Author's name, affiliation, country | Oded Schramm; Microsoft Research |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | effective resistance, commute time, hitting time, difference time,circle packing, triangulation |
| 3. | Subject | Subject classification | 60J10, 52C15. |
| 4. | Description | 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. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | |
| 7. | Date | (YYYY-MM-DD) | 2000-05-05 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | http://ecp.ejpecp.org/article/view/1022 |
| 10. | Identifier | Digital Object Identifier | 10.1214/ECP.v5-1022 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Communications in Probability; Vol 5 |
| 12. | Language | English=en | |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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