{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T02:20:31Z","timestamp":1648779631626},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"An essentially $k$-edge connected graph $G$ is a connected graph such that deleting less than $k$ edges from $G$ cannot result in two nontrivial components.\u00a0In this paper we prove that if an essentially 2-edge-connected graph $G$ satisfies that for any pair of leaves at distance 4 in $G$ there exists another\u00a0leaf of $G$ that has distance 2 to one of them, then the square $G^2$ has a connected even factor with maximum degree at most 4. Moreover we show that, in general, the square of essentially 2-edge-connected graph does not contain a connected even factor with bounded maximum degree.<\/jats:p>","DOI":"10.37236\/5467","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:46:42Z","timestamp":1578653202000},"source":"Crossref","is-referenced-by-count":0,"title":["Connected Even Factors in the Square of Essentially 2-Edge-connected Graph"],"prefix":"10.37236","volume":"24","author":[{"given":"Jan","family":"Ekstein","sequence":"first","affiliation":[]},{"given":"Baoyindureng","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Liming","family":"Xiong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,9,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:49:32Z","timestamp":1579218572000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,8]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/5467","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,8]]}}}