{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815235,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We present a cubic planar hypohamiltonian graph on 70 vertices, improving the best known bound of 94 by Thomassen and derive some consequences concerning longest paths and cycles of planar $3$-connected graphs. We also show that cubic planar hypohamiltonian graphs on $n$ vertices exist for every even number $n\\geq 86$ and that cubic planar hypotraceable graphs exist on $n$ vertices for every even number $n \\geq 356$, settling an open question of Holton and Sheehan.<\/jats:p>","DOI":"10.37236\/572","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:51:17Z","timestamp":1578714677000},"source":"Crossref","is-referenced-by-count":10,"title":["On Cubic Planar Hypohamiltonian and Hypotraceable Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Makoto","family":"Araya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e1bor","family":"Wiener","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,4,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p85\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p85\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:14:16Z","timestamp":1579302856000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p85"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/572","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,4,14]]},"article-number":"P85"}}