{"?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-IO1HCTW9/0494eb11-1e18-42da-b63c-b4237ad56e51/PDF","dcterms:extent":"425 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-IO1HCTW9/c5c6aef1-3ea6-4aa6-9bea-ee9e8b4c5bc0/TEXT","dcterms:extent":"24 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-IO1HCTW9","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":"Suzuki, Yusuke","dc:format":[{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 281-290"}],"dc:identifier":["COBISSID:17833049","ISSN:1855-3966","URN:URN:NBN:SI:doc-IO1HCTW9"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"closed surface"},{"@xml:lang":"en","#text":"generating theorem"},{"@xml:lang":"sl","#text":"izrek o generiranju"},{"@xml:lang":"sl","#text":"kvadrangulacija"},{"@xml:lang":"en","#text":"quadrangulation"},{"@xml:lang":"sl","#text":"sklenjena ploskev"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Cube-contractions in 3-connected quadrangulations|"},"dc:description":[{"@xml:lang":"sl","#text":"A 3-connected quadrangulation of a closed surface is said to be ?$\\mathcal{K}_3^\\prime$?-irreducible if no face-or cube-contraction preserves simplicity and 3-connectedness. In this paper, we prove that a ?$\\mathcal{K}_3^\\prime$?-irreducible quadrangulation of a closed surface except the sphere and the projective plane is either (i) irreducible or (ii) obtained from an irreducible quadrangulation ?$H$? by applying 4-cycle additions to ?$F_0\\subseteq F(H)$? where ?$F(H)$? stands for the set of faces of ?$H$?. We also determine ?$\\mathcal{K}_3^\\prime$?-irreducible quadrangulations of the sphere and the projective plane. These results imply new generating theorems of 3-connected quadrangulations of closed surfaces"},{"@xml:lang":"sl","#text":"Za 3-povezano kvadrangulacijo sklenjene ploskve pravimo, da je ?$\\mathcal{K}_3^\\prime$?-ireducibilna, če nobena skrčtev lic oziroma kock ne ohranja enostavnosti in 3-povezanosti. V tem članku dokažemo, da je ?$\\mathcal{K}_3^\\prime$?-ireducibilna kvadrangulacija sklenjene ploskve z izjemo sfere in projektivne ravnine bodisi (i) ireducibilna bodisi (ii) jo lahko dobimo iz ireducibilne kvadrangulacije ?$H$? z dodajanjem 4-ciklov k ?$F_0\\subseteq F(H)$?, kjer $F(H)$ pomeni množico lic kvadrangulacije ?$H$?. Določimo tudi ?$\\mathcal{K}_3^\\prime$?-ireducibilne kvadrangulacije sfere in projektivne ravnine. Ti rezultati implicirajo nove izreke o generiranju 3-povezanih kvadrangulacij sklenjenih ploskev"}],"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-IO1HCTW9","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-IO1HCTW9"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-IO1HCTW9/0494eb11-1e18-42da-b63c-b4237ad56e51/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-IO1HCTW9/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-IO1HCTW9"}}}}