{"?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-XJJIT4MH/dfa1fc62-1bbb-40ca-b845-5fe28788b7ce/PDF","dcterms:extent":"5360 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-XJJIT4MH/178698fb-ed68-466a-b11a-a40312f48b92/TEXT","dcterms:extent":"29 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-XJJIT4MH","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Jin, Xian'an","Yan, Qi"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 637-652"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18976601","URN:URN:NBN:SI:doc-XJJIT4MH"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"ekstremalni minor"},{"@xml:lang":"en","#text":"extremal minor"},{"@xml:lang":"en","#text":"medial graph"},{"@xml:lang":"sl","#text":"medialni graf"},{"@xml:lang":"sl","#text":"orientacija"},{"@xml:lang":"en","#text":"orientation"},{"@xml:lang":"en","#text":"Petrie dual"},{"@xml:lang":"sl","#text":"Petriejev dual"},{"@xml:lang":"en","#text":"ribbon graph"},{"@xml:lang":"sl","#text":"trakovni graf"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Extremal embedded graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G$? be a ribbon graph and ?$\\mu (G)$? be the number of components of the virtual link formed from ?$G$? as a cellularly embedded graph via the medial construction. In this paper we first prove that ?$\\mu (G) \\leq f(G) + \\gamma (G)$?, where ?$f(G)$? and ?$\\gamma (G)$? are the number of boundary components and Euler genus of ?$G$?, respectively. A ribbon graph is said to be extremal if ?$\\mu (G) = f(G) + \\gamma (G)$?. We then obtain that a ribbon graph is extremal if and only if its Petrial is plane. We introduce a notion of extremal minor and provide an excluded extremal minor characterization for extremal ribbon graphs. We also point out that a related result in the monograph by J. A. Ellis-Monaghan and I. Moffatt Graphs on surfaces. Dualities, polynomials, and knots. New York, NY: Springer (2013) is not correct and prove that two related conjectures raised by S. Huggett and I. Tawfik Ars Math. Contemp. 8, No. 2, 319-335 (2015) hold for more general ribbon graphs"},{"@xml:lang":"sl","#text":"Naj bo ?$G$? trakovni graf in naj bo ?$\\mu (G)$? število komponent virtualne povezave, tvorjene iz grafa ?$G$? kot celično vloženega grafa preko medialne konstrukcije. V članku najprej dokažemo, da je ?$\\mu (G) \\leq f(G) + \\gamma (G)$?, kjer je ?$f(G)$? število robnih komponent, ?$\\gamma (G)$? pa Eulerjev rod grafa ?$G$?. Trakovni graf je ekstremalen, če je ?$\\mu (G) = f(G) + \\gamma (G)$?. Nato pokažemo, da je trakovni graf ekstremalen, če in samo če je njegov Petrial ravninski graf. Vpeljemo pojem ekstremalnega minorja in podamo karakterizacijo ekstremalnih trakovnih grafov z izključenimi ekstremalnimi minorji. Izpostavimo tudi, da soroden rezultat v monografiji Ellis-Monaghana in Moffatta ni pravilen, ter dokažemo, da dve sorodni domnevi, ki sta ju postavila Huggett in Tawfik, veljata za splošnejše trakovne grafe"}],"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-XJJIT4MH","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-XJJIT4MH"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-XJJIT4MH/dfa1fc62-1bbb-40ca-b845-5fe28788b7ce/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-XJJIT4MH/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-XJJIT4MH"}}}}