{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833630,"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 the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if and only if it does not contain a surface of positive genus as a subcomplex and does not have a space minor that is a generalised cone over $K_4$ or $K_{2,3}$.\r\nThis is applied to nested plane embeddings of graphs; that is, plane embeddings constrained by conditions placed on a set of cycles of the graph.<\/jats:p>","DOI":"10.37236\/10539","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:37:35Z","timestamp":1691743055000},"source":"Crossref","is-referenced-by-count":0,"title":["Outerspatial 2-Complexes: Extending the Class of Outerplanar Graphs to Three Dimensions"],"prefix":"10.37236","volume":"30","author":[{"given":"Johannes","family":"Carmesin","sequence":"first","affiliation":[]},{"given":"Tsvetomir","family":"Mihaylov","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,8,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:37:53Z","timestamp":1691743073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i3p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,11]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/10539","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,8,11]]},"article-number":"P3.20"}}