{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:59Z","timestamp":1787322779148,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1362785"],"award-info":[{"award-number":["DMS1362785"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1363136"],"award-info":[{"award-number":["DMS1363136"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/M005038\/1"],"award-info":[{"award-number":["EP\/M005038\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We consider arbitrary graphs $G$ with $n$ vertices and minimum degree at least $\\delta n$ where $\\delta&gt;0$ is constant. (a) If the conductance of $G$ is sufficiently large, then we obtain an asymptotic expression for the cover time $C_G$ of $G$ as the solution to an explicit transcendental equation. (b) If the conductance is not large enough to apply (a), but the mixing time of a random walk on $G$ is of a lesser magnitude than the cover time, then we can obtain an asymptotic deterministic estimate via a decomposition into a bounded number of dense subgraphs with high conductance. (c) If $G$ fits neither (a) nor (b), then we give a deterministic asymptotic (2+o(1))-approximation of $C_G$.<\/jats:p>","DOI":"10.1137\/18m122039x","type":"journal-article","created":{"date-parts":[[2019,7,30]],"date-time":"2019-07-30T12:35:06Z","timestamp":1564490106000},"page":"1374-1389","source":"Crossref","is-referenced-by-count":0,"title":["On the Cover Time of Dense Graphs"],"prefix":"10.1137","volume":"33","author":[{"given":"Colin","family":"Cooper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan M.","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wesley","family":"Pegden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,7,30]]},"reference":[{"key":"atypb1","unstructured":"D. Aldous and J. Fill,\n                      Reversible Markov Chains and Random Walks on Graphs\n                      , manuscripthttps:\/\/www.stat.berkeley.edu\/~aldous\/RWG\/book.html(2002)."},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lov\u00e1sz, and C. Rackoff,\n                      Random walks, universal traversal sequences, and the complexity of maze problems\n                      , in Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, 1979, pp. 218-223.","DOI":"10.1109\/SFCS.1979.34"},{"key":"atypb3","unstructured":"J. Brown and R. Churchill,\n                      Complex Variables and Applications\n                      , 6th ed., McGraw-Hill, New York, 1996."},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"A. K. Chandra, P. Raghavan, W. L. Ruzzo, and R. Smolensky,\n                      The electrical resistance of a graph captures its commute and cover times\n                      , in Proceedings of the 21st ACM Symposium on Theory of Computing, 1989, pp. 574-586.","DOI":"10.1145\/73007.73062"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480103428478"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.05.007"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20151"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20201"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.11.001"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20320"},{"key":"atypb11","first-page":"210","author":"Cooper C.","year":"2011","journal-title":"Proceedings of SIROCCO"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOP822"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2012.175.3.8"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240060106"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240060406"},{"key":"atypb16","unstructured":"J. Kahn, J. H. Kim, L. Lov\u00e1sz, and V. Vu,\n                      The cover time, the blanket time, and the Matthews bound\n                      , in Proceedings of the 41st Annual IEEE Symposium on Foundations of Computing, Redondo Beach, CA, 2000."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01048274"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"D. Levin, Y. Peres, and E. Wilmer,\n                      Markov Chains and Mixing Times\n                      , 2nd ed., AMS, Providence, RI, 2017.","DOI":"10.1090\/mbk\/107"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1145\/331524.331526"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991894"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP997"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v20-4039"},{"key":"atypb23","unstructured":"H. Wilf,\n                      Generatingfunctionology\n                      , Academic Press, New York, 1990."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1214\/18-EJP149"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M122039X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:25:39Z","timestamp":1787318739000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M122039X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M122039X"],"URL":"https:\/\/doi.org\/10.1137\/18m122039x","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}