{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T11:44:32Z","timestamp":1750938272923},"reference-count":8,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4721,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A \u201ccover tour\u201d of a connected graph <jats:italic>G<\/jats:italic> from a vertex <jats:italic>x<\/jats:italic> is a random walk that begins at <jats:italic>x<\/jats:italic>, moves at each step with equal probability to any neighbor of its current vertex, and ends when it has hit every vertex of <jats:italic>G<\/jats:italic>. The cycle <jats:italic>C<\/jats:italic><jats:sub>n<\/jats:sub> is well known to have the curious property that a cover tour from any vertex is equally likely to end at any other vertex; the complete graph <jats:italic>K<\/jats:italic><jats:sub>n<\/jats:sub> shares this property, trivially, by symmetry. Ronald L. Graham has asked whether there are any other graphs with this property; we show that there are not. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170505","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:23:46Z","timestamp":1181240626000},"page":"593-596","source":"Crossref","is-referenced-by-count":4,"title":["A note on the last new vertex visited by a random walk"],"prefix":"10.1002","volume":"17","author":[{"given":"L\u00e1szlo","family":"Lov\u00e1sz","sequence":"first","affiliation":[]},{"given":"Peter","family":"Winkler","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"R.Aleliunas R. M.Karp R. J.Lipton L.Lov\u00e1sz andC.Rackoff Random walks universal traversal sequences and the complexity of maze problems.20th Annual Symposium on Foundations of Computer Science San Juan Puerto Rico (October1979)218\u2013223.","DOI":"10.1109\/SFCS.1979.34"},{"key":"e_1_2_1_3_2","volume-title":"Strength Analysis of Leveling\u2010Type Networks","author":"Borre K.","year":"1974"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"D.Coppersmith P.Doyle P.Raghavan andM.Snir Random walks on weighted graphs and applications to on\u2010line algorithms.Proc. 22nd Annual ACM Symposium on Theory of Computing(1990)369\u2013378.","DOI":"10.1145\/100216.100266"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"M.Dyer A.Frieze andR.Kannan A random polynomial time algorithm for estimating volumes of convex bodies.Proc. 21st Annual ACM Symposium on the Theory of Computing(1989)375\u2013381.","DOI":"10.1145\/73007.73043"},{"key":"e_1_2_1_6_2","unstructured":"R. L.Graham private communication (1989)."},{"key":"e_1_2_1_7_2","unstructured":"A.KarzanovandL.Khachiyan On the conductance of order Markov chains. Technical Report DCS TR 268 Rutgers University New Brunswick NJ June (1990)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"P.TetaliandP.Winkler On a random walk problem arising in self\u2010stabilizing token management. Proc.10th ACM Symp. on the Principles of Distributed Computing(Montreal 1991)273\u2013280.","DOI":"10.1145\/112600.112623"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"D.Zuckerman A technique for lower bounding the cover time.Proc. 22nd Annual ACM Symposium on Theory of Computing(1990)254\u2013259.","DOI":"10.1145\/100216.100249"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170505","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170505","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T07:58:40Z","timestamp":1698307120000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170505"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,11]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1993,11]]}},"alternative-id":["10.1002\/jgt.3190170505"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170505","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,11]]}}}