{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:51Z","timestamp":1753893831464,"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 planar if it has a drawing in which no two edges cross. The Hanani-Tutte Theorem states that a graph is planar if it has a drawing $D$ such that any two edges in $D$ cross an even number of times.\r\nA graph $G$ is a non-separating planar graph if it has a drawing $D$ such that (1) edges do not cross in $D$, and (2) for any cycle $C$ and any two vertices $u$ and $v$ that are not in $C$, $u$ and $v$ are on the same side of $C$ in $D$. Non-separating planar graphs are closed under taking minors and hence have a finite forbidden minor characterisation.\r\nIn this paper, we prove a Hanani-Tutte type theorem for non-separating planar graphs. We use this theorem to prove a stronger version of the strong Hanani-Tutte Theorem for planar graphs, namely that a graph is planar if it has a drawing in which any two disjoint edges cross an even number of times or it has a chordless cycle that enables a suitable decomposition of the graph.<\/jats:p>","DOI":"10.37236\/8903","type":"journal-article","created":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T01:36:32Z","timestamp":1615512992000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Strong Hanani-Tutte Theorem"],"prefix":"10.37236","volume":"28","author":[{"given":"Hooman R.","family":"Dehkordi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Graham","family":"Farr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,2,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p43\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T01:36:33Z","timestamp":1615512993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i1p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,14]]}},"URL":"https:\/\/doi.org\/10.37236\/8903","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,2,26]]},"article-number":"P1.43"}}