{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838556,"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>Thomassen conjectured that triangle-free planar graphs have an exponential number of $3$-colorings. We show this conjecture to be equivalent to the following statement: there exists a positive real\u00a0$\\alpha$ such that whenever $G$ is a planar graph and $A$ is a subset of its edges whose deletion makes\u00a0$G$ triangle-free, there exists a subset\u00a0$A'$ of\u00a0$A$ of size at least\u00a0$\\alpha|A|$ such that $G-(A\\setminus A')$ is $3$-colorable. This equivalence allows us to study restricted situations, where we can prove the statement to be true.<\/jats:p>","DOI":"10.37236\/6736","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:46:16Z","timestamp":1578671176000},"source":"Crossref","is-referenced-by-count":3,"title":["Do Triangle-Free Planar Graphs have Exponentially Many $3$-Colorings?"],"prefix":"10.37236","volume":"24","author":[{"given":"Zden\u011bk","family":"Dvo\u0159\u00e1k","sequence":"first","affiliation":[]},{"given":"Jean-S\u00e9bastien","family":"Sereni","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,9,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:46:27Z","timestamp":1579236387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,8]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6736","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,9,8]]},"article-number":"P3.47"}}