{"?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-48YX15AG/09fa133e-ad01-404d-aec1-083dc0ba6bd1/PDF","dcterms:extent":"384 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-48YX15AG/6d2b0e1f-518d-4d42-abcd-3cca9ee46372/TEXT","dcterms:extent":"30 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-48YX15AG","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2018","dc:creator":["Hou, Jianfeng","Zeng, Qinghou"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:15"},{"@xml:lang":"sl","#text":"str. 147-160"}],"dc:identifier":["COBISSID:18485593","ISSN:1855-3966","URN:URN:NBN:SI:doc-48YX15AG"],"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":"grafi"},{"@xml:lang":"sl","#text":"maksimalni prerez"},{"@xml:lang":"sl","#text":"particija"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Maximum cuts of graphs with forbidden cycles|"},"dc:description":{"@xml:lang":"sl","#text":"Za graf ?$G$?, naj ?$f(G)$? označuje maksimalno število povezav v dvodelnem podgrafu grafa ?$G$?. Za celo število ?$m \\ge 1$? in za množico ?$\\mathcal{H}$? grafov, naj ?$f(m, \\mathcal{H})$? označuje minimalno možno kardinalnost ?$f(G)$?, ko ?$G$? preteče vse grafe z ?$m$? povezavami, ki ne vsebujejo nobenega člana množice ?$\\mathcal{H}$? kot podgrafa. Še posebej, za dani graf ?$H$?, enostavno pišemo ?$f(m, H)$?, za ?$f(m, \\mathcal{H})$?, ko je ?$\\mathcal{H} = \\{H\\}$?. Naj bo ?$r > 4$? fiksno sodo celo število. Alon in drugi (2003) so postavili domnevo, da obstaja pozitivna konstanta ?$c(r)$?, za katero je ?$f(m, C_{r-1}) \\ge m/2 + c(r)m^{r/(r+1)}$? za vse ?$m$?. V tem članku pokažemo, da je ?$f(m, C_{r-1}) \\ge m/2 + c(r)(m^r \\log^4 m)^{1/(r+2)}$? za neko pozitivno konstanto ?$c(r)$? in za vse ?$m$?. Za poljubno določeno celo število ?$s \\ge 2$? študiramo tudi funkcijo ?$f(m, \\mathcal{H})$? za ?$\\mathcal{H} = \\{K_{2,s}, C_5\\}$? in ?$\\mathcal{H} = \\{C_4, C_5,\\dots , C_{r-1}\\}$?, kar oboje izboljšuje rezultat Alona in drugih"},"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-48YX15AG","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-48YX15AG"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-48YX15AG/09fa133e-ad01-404d-aec1-083dc0ba6bd1/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-48YX15AG/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-48YX15AG"}}}}