{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T17:29:20Z","timestamp":1770053360696,"version":"3.49.0"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12261071"],"award-info":[{"award-number":["12261071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation of Qinghai Province","award":["2020-ZJ-920"],"award-info":[{"award-number":["2020-ZJ-920"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:p>Counting maximum matchings in a graph is of great interest in statistical mechanics, solid-state chemistry, theoretical computer science, mathematics, among other disciplines. However, it is a challengeable problem to explicitly determine the number of maximum matchings of general graphs. In this paper, using Gallai\u2013Edmonds structure theorem, we derive a computing formula for the number of maximum matchings in a graph. According to the formula, we obtain an algorithm to enumerate maximum matchings of a graph. In particular, the formula implies that computing the number of maximum matchings of a graph is converted to computing the number of perfect matchings of some induced subgraphs of the graph.<\/jats:p>","DOI":"10.1142\/s0219265924500300","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T04:01:12Z","timestamp":1737432072000},"source":"Crossref","is-referenced-by-count":0,"title":["Enumeration of Maximum Matchings of Graphs"],"prefix":"10.1142","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2488-9775","authenticated-orcid":false,"given":"Tingzeng","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-7179-4206","authenticated-orcid":false,"given":"Xiaolin","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1033-2386","authenticated-orcid":false,"given":"Huazhong","family":"L\u00fc","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,1,20]]},"reference":[{"key":"S0219265924500300BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.2725"},{"key":"S0219265924500300BIB002","doi-asserted-by":"publisher","DOI":"10.26493\/1855-3974.851.167"},{"key":"S0219265924500300BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22244"},{"key":"S0219265924500300BIB004","doi-asserted-by":"publisher","DOI":"10.1063\/1.1703953"},{"key":"S0219265924500300BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2015.09.027"},{"key":"S0219265924500300BIB006","author":"Lov\u00e1sz L.","year":"2009","journal-title":"American Math. Soc."},{"key":"S0219265924500300BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(79)90044-6"},{"key":"S0219265924500300BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.03.065"},{"key":"S0219265924500300BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2020.102082"},{"key":"S0219265924500300BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/S0196-8858(03)00097-6"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265924500300","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T07:00:08Z","timestamp":1770015608000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219265924500300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,20]]},"references-count":10,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["10.1142\/S0219265924500300"],"URL":"https:\/\/doi.org\/10.1142\/s0219265924500300","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,20]]},"article-number":"2450030"}}