{"?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-FLBNZGZF/1722aafb-6ba1-4807-8df6-8c905b4c01c4/PDF","dcterms:extent":"333 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-FLBNZGZF/9088e8ea-234f-46b1-a3de-6e6b07e4339c/TEXT","dcterms:extent":"34 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-FLBNZGZF","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":["Schaefer, Alex","Zaslavsky, Thomas"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 625-639"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18822745","URN:URN:NBN:SI:doc-FLBNZGZF"],"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":"negative cycle vector"},{"@xml:lang":"sl","#text":"permutabilno prirejanje"},{"@xml:lang":"en","#text":"permutable matching"},{"@xml:lang":"sl","#text":"predznačeni graf"},{"@xml:lang":"en","#text":"signed graph"},{"@xml:lang":"sl","#text":"vektor negativnih ciklov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The dimension of the negative cycle vectors of a signed graph|"},"dc:description":[{"@xml:lang":"sl","#text":"A signed graph is a graph ?$\\Gamma$? with edges labeled \"?$+$?\" and \"?$-$?\". The sign of a cycle is the product of its edge signs. Let ?$\\mathrm{SpecC}(\\Gamma)$? denote the list of lengths of cycles in ?$\\Gamma$?. We equip each signed graph with a vector whose entries are the numbers of negative ?$k$?-cycles for ?$k \\in \\mathrm{SpecC}(\\Gamma)$?. These vectors generate a subspace of ?$\\mathbb{R}^{|\\mathrm{SpecC}(\\Gamma)|}$?. Using matchings with a strong permutability property, we provide lower bounds on the dimension of this space; in particular, we show for complete graphs, complete bipartite graphs, and a few other graphs that this space is all of ?$\\mathbb{R}^{|\\mathrm{SpecC}(\\Gamma)|}$?"},{"@xml:lang":"sl","#text":"Predznačeni graf je graf ?$\\Gamma$?, katerega povezave so označene s \"?$+$?\" in \"?$-$?\". Predznak cikla je produkt predznakov njegovih povezav. Naj ?$\\mathrm{SpecC}(\\Gamma)$? označuje seznam dolžin ciklov v grafu ?$\\Gamma$?. Vsakemu predznačenemu grafu priredimo vektor, katerega komponente so števila negativnih ?$k$?-ciklov za ?$k \\in \\mathrm{SpecC}(\\Gamma)$?. Ti vektorji generirajo podprostor prostora ?$\\mathbb{R}^{|\\mathrm{SpecC}(\\Gamma)|}$?. Z uporabo prirejanj s krepko permutabilnostno lastnostjo dobimo spodnje meje za dimenzijo tega prostora in pokažemo, da je za polne grafe, polne dvodelne grafe in še nekaj drugih grafov ta prostor enak celotnemu prostoru ?$\\mathbb{R}^{|\\mathrm{SpecC}(\\Gamma)|}$?"}],"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-FLBNZGZF","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-FLBNZGZF"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-FLBNZGZF/1722aafb-6ba1-4807-8df6-8c905b4c01c4/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-FLBNZGZF/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-FLBNZGZF"}}}}