{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836947,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We introduce a common generalization of the strong Hanani\u2013Tutte theorem and the weak Hanani\u2013Tutte theorem: if a graph $G$ has a drawing $D$ in the plane where every pair of independent edges crosses an even number of times, then $G$ has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in $D$. The theorem is implicit in the proof of the strong Hanani\u2013Tutte theorem by Pelsmajer, Schaefer and \u0160tefankovi\u010d. We give a new, somewhat simpler proof.<\/jats:p>","DOI":"10.37236\/6663","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:50:54Z","timestamp":1578671454000},"source":"Crossref","is-referenced-by-count":1,"title":["Unified Hanani\u2013Tutte Theorem"],"prefix":"10.37236","volume":"24","author":[{"given":"Radoslav","family":"Fulek","sequence":"first","affiliation":[]},{"given":"Jan","family":"Kyn\u010dl","sequence":"additional","affiliation":[]},{"given":"D\u00f6m\u00f6t\u00f6r","family":"P\u00e1lv\u00f6lgyi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:50:51Z","timestamp":1579236651000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,28]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6663","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,7,28]]},"article-number":"P3.18"}}