{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:21:04Z","timestamp":1761675664996},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p> It is well known that any two longest paths in a connected graph share a vertex. It is also known that there are connected graphs where 7 longest paths do not share a common vertex. It was conjectured that any three longest paths in a connected graph have a vertex in common. In this note we prove the conjecture for outerplanar graphs and give sufficient conditions for the conjecture to hold in general. <\/jats:p>","DOI":"10.1142\/s1793830909000038","type":"journal-article","created":{"date-parts":[[2009,4,8]],"date-time":"2009-04-08T08:55:25Z","timestamp":1239180925000},"page":"115-120","source":"Crossref","is-referenced-by-count":6,"title":["WHEN DO THREE LONGEST PATHS HAVE A COMMON VERTEX?"],"prefix":"10.1142","volume":"01","author":[{"given":"MARIA","family":"AXENOVICH","sequence":"first","affiliation":[{"name":"412 Carver Hall, Iowa State University, Ames, IA 50011, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548304006145"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.07.013"},{"key":"rf3","first-page":"43","volume":"29","author":"Klav\u017ear S.","journal-title":"Ars Combin."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300002170"},{"key":"rf5","series-title":"Mathematics and Its Applications (East European Series)","volume-title":"Cycles and Bridges in Graphs","volume":"49","author":"Voss H.-J.","year":"1991"},{"key":"rf6","first-page":"1","volume":"28","author":"Zamfirescu T.","journal-title":"An. Univ. Craiova Ser. Mat. Inform."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830909000038","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T02:17:27Z","timestamp":1565144247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830909000038"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":6,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2009,3]]}},"alternative-id":["10.1142\/S1793830909000038"],"URL":"https:\/\/doi.org\/10.1142\/s1793830909000038","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}