{"?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-WE8D4U05/ba6cbd9a-51da-4340-8a90-aefbd17ad828/PDF","dcterms:extent":"255 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-WE8D4U05/26e72e91-db3f-4d06-8450-863bd8403c1a/TEXT","dcterms:extent":"12 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-WE8D4U05","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Petruševski, Mirko","Škrekovski, Riste"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 317-322"}],"dc:identifier":["ISSN:1855-3966","COBISSID:2048439059","URN:URN:NBN:SI:doc-WE8D4U05"],"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":"aciklično število"},{"@xml:lang":"sl","#text":"induciran gozd"},{"@xml:lang":"sl","#text":"ožina"},{"@xml:lang":"sl","#text":"ravninski graf"},{"@xml:lang":"sl","#text":"teorija grafov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A note on acyclic number of planar graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"The acyclic number ?$a(G)$? of a graph ?$G$? is the maximum order of an induced forest in ?$G$?. The purpose of this short paper is to propose a conjecture that ?$a(G)\\geq \\left( 1-\\frac{3}{2g}\\right)n$? holds for every planar graph ?$G$? of girth ?$g$? and order ?$n$?, which captures three known conjectures on the topic. In support of this conjecture, we prove a weaker result that ?$a(G)\\geq \\left( 1-\\frac{3}{g} \\right)n$? holds. In addition, we give a construction showing that the constant ?$\\frac{3}{2}$? from the conjecture cannot be decreased"},{"@xml:lang":"sl","#text":"Aciklično število ?$a(G)$? grafa ?$G$? je maksimalni red induciranega gozda v ?$G$?. Namen tega kratkega članka je predstavitev domneve, da ?$a(G)\\geq \\left( 1-\\frac{3}{2g}\\right)n$? velja za vsak ravninski graf ?$G$? ožine ?$g$? in reda ?$n$?, ki obsega tri znane hipoteze s tega področja. V podporo tej domnevi dokažemo šibkejši rezultat, da velja ?$a(G)\\geq \\left( 1-\\frac{3}{g} \\right)n$?. Poleg tega podamo konstrukcijo, ki pokaže, da konstante ?$\\frac{3}{2}$? iz te hipoteze ni mogoče zmanjšati"}],"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-WE8D4U05","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-WE8D4U05"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-WE8D4U05/ba6cbd9a-51da-4340-8a90-aefbd17ad828/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-WE8D4U05/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-WE8D4U05"}}}}