{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,26]],"date-time":"2023-08-26T13:12:08Z","timestamp":1693055528280},"reference-count":9,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2021,10,18]],"date-time":"2021-10-18T00:00:00Z","timestamp":1634515200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2022,4]]},"abstract":"Abstract<\/jats:title>It is proved that for , the number of perfect matchings in a simple connected cubic graph on vertices is at most , with being the \u2010th Fibonacci number. The unique extremal graph is characterized as well. In addition, it is shown that the number of perfect matchings in any cubic graph equals the expected value of a random variable defined on all 2\u2010colorings of edges of . Finally, an improved lower bound on the maximum number of cycles in a cubic graph is provided.<\/jats:p>","DOI":"10.1002\/jgt.22759","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T19:08:27Z","timestamp":1634756907000},"page":"671-690","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Connected cubic graphs with the maximum number of perfect matchings"],"prefix":"10.1002","volume":"99","author":[{"given":"Peter","family":"Horak","sequence":"first","affiliation":[{"name":"School of Interdisciplinary Arts and Sciences University of Washington Tacoma Washington USA"}]},{"given":"Dongryul","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics Stanford University Stanford California USA"}]}],"member":"311","published-online":{"date-parts":[[2021,10,18]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01444208"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20290"},{"issue":"1","key":"e_1_2_7_4_1","article-title":"The maximum number of perfect matchings in graphs with a given degree sequence","volume":"15","author":"N. Alon and S. Friedland","year":"2008","journal-title":"Electron. J. Combin"},{"key":"e_1_2_7_5_1","first-page":"27","article-title":"Certain properties of nonnegative matrices and their permanents","volume":"211","author":"Br\u00e8gman L. M.","year":"1973","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"e_1_2_7_6_1","first-page":"289","article-title":"On the maximum number of cycles in a graph","volume":"11","author":"Entringer R. C.","year":"1981","journal-title":"Ars Combin"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.03.015"},{"key":"e_1_2_7_8_1","doi-asserted-by":"crossref","unstructured":"G.Galbiati An exact upper bound to the maximum number of perfect matchings in cubic pseudographs Calcolo.18(1982) no.4 361\u2013370.","DOI":"10.1007\/BF02576436"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2014.04.019"},{"key":"e_1_2_7_10_1","doi-asserted-by":"crossref","unstructured":"L.Lov\u00e1szandM. D.Plummer Matching theory. AMS Chelsea Publishing Providence RI 2009. Corrected reprint of the 1986 original [MR0859549].","DOI":"10.1090\/chel\/367"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22759","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/jgt.22759","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22759","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,26]],"date-time":"2023-08-26T00:04:22Z","timestamp":1693008262000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22759"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,18]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["10.1002\/jgt.22759"],"URL":"https:\/\/doi.org\/10.1002\/jgt.22759","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,18]]},"assertion":[{"value":"2021-04-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-09-15","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-10-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}