{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:02Z","timestamp":1753893842204,"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>A graph is hypohamiltonian if it is not hamiltonian but every vertex-deleted subgraph is. In this paper we study hypohamiltonian snarks \u2013 cubic hypohamiltonian graphs with chromatic index 4. We describe a method, based on superposition of snarks, which produces new hypohamiltonian snarks from old ones. By choosing suitable ingredients we can achieve that the resulting graphs are cyclically $5$-connected or $6$-connected.  Previously, only three sporadic hypohamiltonian snarks with cyclic connectivity 5 had been found, while the flower snarks of Isaacs were the only known family of cyclically 6-connected hypohamiltonian snarks.  Our method produces hypohamiltonian snarks with cyclic connectivity $5$ and $6$ for all but finitely many even orders.<\/jats:p>","DOI":"10.37236\/936","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:51:54Z","timestamp":1578718314000},"source":"Crossref","is-referenced-by-count":5,"title":["Constructing Hypohamiltonian Snarks with Cyclic Connectivity $5$ and $6$"],"prefix":"10.37236","volume":"14","author":[{"given":"Edita","family":"M\u00e1\u010dajov\u00e1","sequence":"first","affiliation":[]},{"given":"Martin","family":"\u0160koviera","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:04:34Z","timestamp":1579320274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/936","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,29]]},"article-number":"R18"}}