{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-F2X1HOEV/398B3036-ED0D-47E4-8CF9-08FAFE32F2F0/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-F2X1HOEV/8c41449f-f19c-4937-b091-624a082be3eb/PDF","dcterms:extent":"411 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-F2X1HOEV/d1488320-f93a-4720-a67b-ff90695c2a58/TEXT","dcterms:extent":"49 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-F2X1HOEV","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2012","dc:creator":["Boutin, Debra L.","Cockburn, Sally","Dean, Alice M.","Margea, Andrei M."],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:5"},{"@xml:lang":"sl","#text":"str. 269-288"}],"dc:identifier":["COBISSID:16275801","ISSN:1855-3966","URN:URN:NBN:SI:doc-F2X1HOEV"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"sl","#text":"delno urejena množica"},{"@xml:lang":"en","#text":"geometric graph"},{"@xml:lang":"sl","#text":"geometrijski graf"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"sl","#text":"homomorfizem"},{"@xml:lang":"en","#text":"homomorphism"},{"@xml:lang":"en","#text":"poset"},{"@xml:lang":"sl","#text":"teorija grafov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Posets of geometric graphs|"},"dc:description":{"@xml:lang":"sl","#text":"A geometric graph ?$\\overline{G}$? is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call ?$\\overline{G}$? a geometric realization of the underlying abstract graph ?$G$?. A geometric homomorphism ?$f: \\overline{G} \\to \\overline{H}$? is a vertex map that preserves adjacencies and crossings (but not necessarily non-adjacencies or non-crossings). This work uses geometric homomorphisms to introduce a partial order on the set of isomorphism classes of geometric realizations of an abstract graph ?$G$?. Set ?$\\overline{G} \\preceq \\widehat{G}$? if ?$\\overline{G}$? and ?$\\widehat{G}$? are geometric realizations of ?$G$? and there is a vertex-injective geometric homomorphism ?$f: \\overline{G} \\to \\widehat{G}$?. This paper develops tools to determine when two geometric realizations are comparable. Further, for ?$3 \\le n \\le 6$?, this paper provides the isomorphism classes of geometric realizations of ?$P_n$?, ?$C_n$? and ?$K_n$?, as well as the Hasse diagrams of the geometric homomorphism posets (resp., ?$\\mathcal{P}_n, \\mathcal{C}_n, \\mathcal{K}_n$?) of these graphs. The paper also provides the following results for general ?$n$?: each of ?$\\mathcal{P}_n$? and ?$\\mathcal{C}_n$? has a unique minimal element and a unique maximal element; if ?$k \\le n$? then ?$\\mathcal{P}_k$? (resp., ?$\\mathcal{C}_k$?) is a subposet of ?$\\mathcal{P}_n$? (resp., ?$\\mathcal{C}_n$?); and ?$\\mathcal{K}_n$? contains a chain of length ?$n - 2$?"},"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:DOC-F2X1HOEV","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-F2X1HOEV"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-F2X1HOEV/398B3036-ED0D-47E4-8CF9-08FAFE32F2F0/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-F2X1HOEV/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-F2X1HOEV"}}}}