{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835041,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>If $X$ is a collection of edges in a graph $G$, let $G\/X$ denote the contraction of $X$. Following a question of Oxley and a conjecture of Oporowski, we prove that every projective planar graph $G$ admits an edge partition $\\{X,Y\\}$ such that $G\/X$ and $G\/Y$ have tree-width at most three. We prove that every toroidal graph $G$ admits an edge partition $\\{X,Y\\}$ such that $G\/X$ and $G\/Y$ have tree-width at most three and four, respectively.<\/jats:p>","DOI":"10.37236\/2534","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:05:03Z","timestamp":1578697503000},"source":"Crossref","is-referenced-by-count":0,"title":["Bounding Tree-Width via Contraction on the Projective Plane and Torus."],"prefix":"10.37236","volume":"22","author":[{"given":"Evan","family":"Morgan","sequence":"first","affiliation":[]},{"given":"Bogdan","family":"Oporowski","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:09:28Z","timestamp":1579255768000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/2534","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,10,16]]},"article-number":"P4.5"}}