{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T17:06:35Z","timestamp":1771866395777,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A well-known conjecture of Thomassen states that every cycle of maximum order in a $3$-connected graph contains a chord. While many partial results towards this conjecture have been obtained, the conjecture itself remains unsolved. In this paper, we prove a stronger result without a connectivity assumption for graphs of high minimum degree, which shows Thomassen's conjecture holds in that case. This result is within a constant factor of best possible. In the process of proving this, we prove a more general result showing that large minimum degree forces a large difference between the order of the largest cycle and the order of the largest chordless cycle.<\/jats:p>","DOI":"10.37236\/7152","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:42:56Z","timestamp":1578652976000},"source":"Crossref","is-referenced-by-count":5,"title":["A Cycle of Maximum Order in a Graph of High Minimum Degree has a Chord"],"prefix":"10.37236","volume":"24","author":[{"given":"Daniel J.","family":"Harvey","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,11,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:42:06Z","timestamp":1579218126000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,24]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7152","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,24]]},"article-number":"P4.33"}}