{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:59:34Z","timestamp":1778720374439,"version":"3.51.4"},"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>The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the paper. In the second part the theorem is applied to show that interesting combinatorial sets related to a planar graph have lattice structure: Eulerian orientations, spanning trees and Schnyder woods. For the Schnyder wood application some additional theory has to be developed. In particular it is shown that a Schnyder wood for a planar graph induces a Schnyder wood for the dual. <\/jats:p>","DOI":"10.37236\/1768","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:23:22Z","timestamp":1578720202000},"source":"Crossref","is-referenced-by-count":45,"title":["Lattice Structures from Planar Graphs"],"prefix":"10.37236","volume":"11","author":[{"given":"Stefan","family":"Felsner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2004,2,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:04:42Z","timestamp":1579323882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1768","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,14]]},"article-number":"R15"}}