{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:00Z","timestamp":1753893840916,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove that every locally Hamiltonian graph with $n$ vertices and possibly with multiple edges has at least $3n-6$ edges with equality if and only if it triangulates the sphere. As a consequence, every edge-maximal embedding of a graph $G$ on some 2-dimensional surface $\\Sigma$ (not necessarily compact) has at least $3n-6$ edges with equality if and only if $G$ also triangulates the sphere. If, in addition, $G$ is simple, then for each vertex $v$, the cyclic ordering of the edges around $v$ on $\\Sigma$ is the same as the clockwise or anti-clockwise orientation around $v$ on the sphere. If $G$ contains no complete graph on 4 vertices, then the face-boundaries are the same in the two embeddings.<\/jats:p>","DOI":"10.37236\/9286","type":"journal-article","created":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:19:41Z","timestamp":1590718781000},"source":"Crossref","is-referenced-by-count":2,"title":["Locally Hamiltonian Graphs and Minimal Size of Maximal Graphs on a Surface"],"prefix":"10.37236","volume":"27","author":[{"given":"James","family":"Davies","sequence":"first","affiliation":[]},{"given":"Carsten","family":"Thomassen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,5,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p25\/8082","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p25\/8082","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:19:41Z","timestamp":1590718781000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,29]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/9286","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,5,29]]},"article-number":"P2.25"}}