{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:14Z","timestamp":1753893854802,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph of order $n$ is $p$-factor-critical, where $p$ is an integer of the same parity as $n$, if the removal of any set of $p$ vertices results in a graph with a perfect matching. 1-factor-critical graphs and 2-factor-critical graphs are well-known\u00a0factor-critical graphs and bicritical graphs, respectively. It is known that if a connected vertex-transitive graph has odd order, then it is factor-critical, otherwise it is elementary bipartite or bicritical. In this paper, we show that a connected vertex-transitive non-bipartite graph of even order at least 6 is 4-factor-critical if and only if its degree is at least 5. This result implies that each connected non-bipartite Cayley graph of even order and degree at least 5 is 2-extendable.<\/jats:p>","DOI":"10.37236\/4807","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:51:50Z","timestamp":1578689510000},"source":"Crossref","is-referenced-by-count":0,"title":["4-Factor-Criticality of Vertex-Transitive Graphs"],"prefix":"10.37236","volume":"23","author":[{"given":"Wuyang","family":"Sun","sequence":"first","affiliation":[]},{"given":"Heping","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,7,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:27:18Z","timestamp":1579238838000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,8]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/4807","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,7,8]]},"article-number":"P3.1"}}