{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T03:09:59Z","timestamp":1719803399913},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"Let $G$ be a connected graph with an even number of edges.\u00a0We show that if the subgraph of $G$ induced by the vertices of odd\u00a0degree has a perfect matching, then the line graph of $G$ has a\u00a0$2$-factor whose connected components are cycles of even length (an\u00a0even $2$-factor). For a cubic graph $G$, we also give a necessary\u00a0and sufficient condition so that the corresponding line graph $L(G)$ has an even cycle decomposition of index $3$, i.e., the edge-set of\u00a0$L(G)$ can be partitioned into three $2$-regular subgraphs whose\u00a0connected components are cycles of even length. The more general\u00a0problem of the existence of even cycle decompositions of index $m$\u00a0in $2d$-regular graphs is also addressed.<\/jats:p>","DOI":"10.37236\/5660","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:44:38Z","timestamp":1578653078000},"source":"Crossref","is-referenced-by-count":2,"title":["Even Cycles and Even 2-Factors in the Line Graph of a Simple Graph"],"prefix":"10.37236","volume":"24","author":[{"given":"Arrigo","family":"Bonisoli","sequence":"first","affiliation":[]},{"given":"Simona","family":"Bonvicini","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,10,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:44:59Z","timestamp":1579218299000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/5660","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,20]]}}}