{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:21Z","timestamp":1753893861304,"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>A partial cube is a graph having an isometric embedding in a\u00a0hypercube. Partial cubes are characterized by a natural equivalence\u00a0relation on the edges, whose classes are called zones. The\u00a0number of zones determines the minimal dimension of a hypercube\u00a0in which the graph can be embedded. We consider the problem of\u00a0covering the vertices of a partial cube with the minimum number of\u00a0zones. The problem admits several special cases, among which are the following:cover the cells of a line arrangement with a minimum number of lines,select a smallest subset of edges in a graph such that for every acyclic orientation, there exists a selected edge that can be flipped without creating a cycle,find a smallest set of incomparable pairs of elements in a poset such that in every linear extension, at least one such pair is consecutive,find a minimum-size fibre in a bipartite poset.We give upper and lower bounds on the worst-case minimum size of a covering by zones\u00a0in several of those cases. We also consider the computational complexity of those problems, and establish some hardness results.<\/jats:p>","DOI":"10.37236\/5076","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:26:19Z","timestamp":1578669979000},"source":"Crossref","is-referenced-by-count":0,"title":["Covering Partial Cubes with Zones"],"prefix":"10.37236","volume":"22","author":[{"given":"Jean","family":"Cardinal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Felsner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,8,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:13:13Z","timestamp":1579255993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,28]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/5076","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,8,28]]},"article-number":"P3.31"}}