{"?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-91ZUQR2E/6b2436cb-946d-423f-a5a6-3ee223fc82cc/PDF","dcterms:extent":"1078 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-91ZUQR2E/8d89a74c-a281-41b9-b1b8-996466d3c2be/TEXT","dcterms:extent":"62 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-91ZUQR2E/19a6a2c2-97b9-4270-a58f-49be08ef67c1/PDF","dcterms:extent":"94 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-91ZUQR2E/39c62503-948d-48ae-a513-408e9593dbc0/TEXT","dcterms:extent":"3 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-91ZUQR2E","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":["Abrams, Lowell","Berman, Yosef","Faber, Vance","Murphy, Michael"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.05"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-32"}],"dc:identifier":["DOI:10.26493/1855-3974.3080.a2f","ISSN:1855-3974","COBISSID_HOST:289313283","URN:URN:NBN:SI:doc-91ZUQR2E"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"sl","#text":"imerzija"},{"@xml:lang":"en","#text":"immersion"},{"@xml:lang":"sl","#text":"kvadrangulacija"},{"@xml:lang":"en","#text":"quadrangulation"},{"@xml:lang":"sl","#text":"sferična vložitev"},{"@xml:lang":"en","#text":"spherical embedding"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Which cubic graphs have quadrangulated spherical immersions?|"},"dc:description":[{"@xml:lang":"sl","#text":"We consider spherical quadrangulations – spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 – in which all vertices have degree 3 or 4. Interpreting each degree 4 vertex as a crossing, these embeddings can also be thought of as transversal immersions of cubic graphs which we refer to as the extracted graphs. We also consider quadrangulations of the disk in which interior vertices have degree 3 or 4 and boundary vertices have degree 2 or 3. First, we classify all such quadrangulations of the disk. Then, we provide four methods for constructing spherical quadrangulations, two of which use quadrangulations of the disk as input. Two of these methods provide one-parameter families of quadrangulations, for which we prove that the sequence of isomorphism types of extracted graphs is periodic. We close with a description of computer computations which yielded spherical quadrangulations for all but three cubic multigraphs on eight vertices"},{"@xml:lang":"sl","#text":"Obravnavamo sferične kvadrangulacije – sferične vložitve multigrafov, po možnosti z zankami, tako da ima vsaka ploskev obhodno dolžino 4 – v kateri imajo vsa vozlišča stopnjo 3 ali 4. Pri interpretaciji vsakega vozlišca stopnje 4 kot presecišča lahko te vložitve razumemo tudi kot precne imerzije kubičnih grafov, ki jih imenujemo izvlečeni grafi. Obravnavamo tudi kvadrangulacije diska, pri katerih imajo notranja vozlišca stopnjo 3 ali 4, vozlišca na meji pa stopnjo 2 ali 3. Najprej razvrstimo vse takšne kvadrangulacije diska. Nato podamo štiri metode za konstrukcijo sfericnih kvadrangulacij, pri čemer dve od teh metod uporabljata kvadrangulacije diska kot vhodne podatke. Dve izmed metod dasta enoparametricni družini kvadrangulacij, za kateri dokažemo, da je zaporedje izomorfnih tipov izvlečenih grafov periodično. Članek zaključimo z opisom računalniških izračunov, ki so dali sferične kvadrangulacije za vse razen tri kubične multigrafe z osmimi vozlišči"}],"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-91ZUQR2E","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-91ZUQR2E"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-91ZUQR2E/6b2436cb-946d-423f-a5a6-3ee223fc82cc/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-91ZUQR2E/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-91ZUQR2E"}}}}