{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:07:12Z","timestamp":1758823632079,"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>In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three $3$-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four $3$-cuts have a hamiltonian path. It is well known that for each $k\\ge 6$ non-hamiltonian polyhedra with $k$ $3$-cuts exist. We give computational results on lower bounds on the order of a possible non-hamiltonian polyhedron for the remaining open cases of polyhedra with four or five $3$-cuts.<\/jats:p>","DOI":"10.37236\/7771","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:11:51Z","timestamp":1578640311000},"source":"Crossref","is-referenced-by-count":10,"title":["Polyhedra with Few 3-Cuts are Hamiltonian"],"prefix":"10.37236","volume":"26","author":[{"given":"G.","family":"Brinkmann","sequence":"first","affiliation":[]},{"given":"C. T.","family":"Zamfirescu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p39\/7798","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p39\/7798","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:17:42Z","timestamp":1579234662000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7771","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,3,8]]},"article-number":"P1.39"}}