{"id":145252,"date":"2000-01-01T00:00:00","date_gmt":"2000-01-01T00:00:00","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/on-the-cover-time-of-planar-graphs\/"},"modified":"2018-10-16T19:57:23","modified_gmt":"2018-10-17T02:57:23","slug":"on-the-cover-time-of-planar-graphs","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/on-the-cover-time-of-planar-graphs\/","title":{"rendered":"On the cover time of planar graphs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>\u00a0The 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.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0The 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 [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Electron. Comm. Probab.","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Electron. Comm. 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