{"?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-NC5HFPJD/55805715-3A4E-4707-A895-3712B01826C0/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-NC5HFPJD/1ce6947a-40c5-4bd2-9b07-7619e156ce92/PDF","dcterms:extent":"211 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-NC5HFPJD/2a19f431-99db-47a5-9988-4eae116655cc/TEXT","dcterms:extent":"16 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-NC5HFPJD","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":["Levit, Vadim E.","Mandrescu, Eugen"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:5"},{"@xml:lang":"sl","#text":"str. 325-331"}],"dc:identifier":["COBISSID:16277849","ISSN:1855-3966","URN:URN:NBN:SI:doc-NC5HFPJD"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"core"},{"@xml:lang":"sl","#text":"enociklični graf"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"sl","#text":"jedro grafa"},{"@xml:lang":"sl","#text":"König-Egervárijev graf"},{"@xml:lang":"en","#text":"König-Egerváry graph"},{"@xml:lang":"sl","#text":"maksimalna neodvisna množica"},{"@xml:lang":"en","#text":"matching"},{"@xml:lang":"en","#text":"maximum independent set"},{"@xml:lang":"sl","#text":"prirejanje"},{"@xml:lang":"sl","#text":"teorija grafov"},{"@xml:lang":"en","#text":"unicyclic graph"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the core of a unicyclic graph|"},"dc:description":{"@xml:lang":"sl","#text":"A set ?$S \\subseteq V$? is independent in a graph ?$G = (V, E)$? if no two vertices from ?$S$? are adjacent. By core?$(G)$? we mean the intersection of all maximum independent sets. The independence number ?$\\alpha(G)$? is the cardinality of a maximum independent set, while ?$\\mu(G)$? is the size of a maximum matching in ?$G$?. A connected graph having only one cycle, say ?$C$?, is a unicyclic graph. In this paper we prove that if ?$G$? is a unicyclic graph of order ?$n$? and T$n - 1 = \\alpha(G) + \\mu(G)$T, then core?$(G)$? coincides with the union of cores of all trees in ?$G - C$?"},"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-NC5HFPJD","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-NC5HFPJD"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-NC5HFPJD/55805715-3A4E-4707-A895-3712B01826C0/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-NC5HFPJD/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-NC5HFPJD"}}}}