{"?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-VLFA6YN7/c71bb415-64ea-4fee-bff6-8ac323fd977f/PDF","dcterms:extent":"185 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-VLFA6YN7/cf11bb76-86fa-4c32-a168-ecc65a5ec939/TEXT","dcterms:extent":"9 KB"}],"edm:TimeSpan":{"@rdf:about":"1977-2026","edm:begin":{"@xml:lang":"en","#text":"1977"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-VLFA6YN7","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-EE5UIE2V"},{"@xml:lang":"sl","#text":"Informatica (Ljubljana)"}],"dcterms:issued":"2006","dc:creator":"Mohar, Bojan","dc:format":[{"@xml:lang":"sl","#text":"številka:3"},{"@xml:lang":"sl","#text":"letnik:30"},{"@xml:lang":"sl","#text":"str. 301-303"}],"dc:identifier":["ISSN:0350-5596","COBISSID:20379431","URN:URN:NBN:SI:doc-VLFA6YN7"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Slovensko društvo Informatika"},"dc:subject":[{"@xml:lang":"sl","#text":"matematika"},{"@xml:lang":"en","#text":"mathematics"},{"@xml:lang":"sl","#text":"ravninski grafi"},{"@xml:lang":"sl","#text":"Riskinova teza"},{"@xml:lang":"sl","#text":"teorija grafov"},{"@rdf:resource":"http://www.wikidata.org/entity/Q395"}],"dcterms:temporal":{"@rdf:resource":"1977-2026"},"dc:title":{"@xml:lang":"sl","#text":"On the crossing number of almost planar graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"If ?$G$? is a plane graph and ?$x,y \\in V(G)$?, then the dual distance of ?$x$? and ?$y$? is equal to the maximum number of crossings of ?$G$? with a curve in the plane joining ?$x$? and ?$y$?. Riskin proved that if ?$G_0$? is a 3-connected cubic planar graph, and ?$x, y$? are its vertices at dual distance ?$d$?, then the crossing number of the graph ?$G_0 + xy$? is equal to ?$d$?. Riskin asked if his results holds for arbitrary 3-connected planar graphs. We show that this is not the case (not even for every 5-connected planar graph ?$G_0$?)"},{"@xml:lang":"sl","#text":"Če je ?$G$? grad, vložen v ravnini, in sta ?$x$? in ?$y$? in njegovi vozlišči, definiramo ?$d(x,y)$? kot minimalno število točk na ?$G$?, ki jih sekajo krivulje od ?$x$? do ?$y$?. Riskin je dokazal, da je v primeru ravninskega 3-povezanega kubičnega grafa ?$G_0$? število ?$d(x,y)$? enako prekrižnemu številu grafa ?$G_0+xy$?. Vprašal je, če enako velja tudi v primeru, ko ?$G_0$? ni kubičen graf. V delu je dokazano, da to ni res, tudi če dodatno privzamemo, da je ?$G_0$? 5-povezan"}],"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-VLFA6YN7","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-VLFA6YN7"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-VLFA6YN7/c71bb415-64ea-4fee-bff6-8ac323fd977f/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"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":"Slovensko društvo Informatika"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-VLFA6YN7/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-VLFA6YN7"}}}}