{"?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-5M5H6R3X/dbb6a7bb-97e6-49b4-b97a-7611f1b03172/PDF","dcterms:extent":"635 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5M5H6R3X/59b7a2f2-114d-47ab-8166-a581b696f398/TEXT","dcterms:extent":"67 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-5M5H6R3X","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":["Cho, Eun-Kyung","Culver, Eric","Hartke, Stephen G.","Iršič Chenoweth, Vesna"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.08"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-32"}],"dc:identifier":["DOI:10.26493/1855-3974.3389.86c","ISSN:1855-3974","COBISSID_HOST:289327619","URN:URN:NBN:SI:doc-5M5H6R3X"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"sl","#text":"dominacija"},{"@xml:lang":"en","#text":"domination"},{"@xml:lang":"sl","#text":"podkubični ravninski graf"},{"@xml:lang":"en","#text":"subcubic planar graph"},{"@xml:lang":"en","#text":"upper bound"},{"@xml:lang":"sl","#text":"zgornja meja"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Domination of subcubic planar graphs with large girth|"},"dc:description":[{"@xml:lang":"sl","#text":"Since Reed conjectured in 1996 that the domination number of a connected cubic graph of order n is at most ?1/3n?, the domination number of cubic graphs has been extensively studied. It is now known that the conjecture is false in general, but Henning and Dorbec showed that it holds for graphs with girth at least 9. Zhu and Wu stated an analogous conjecture for 2-connected cubic planar graphs. In this paper, we present a new upper bound for the domination number of subcubic planar graphs: if G is a subcubic planar graph with girth at least 8, then ?(G) < n0 + 3/4 n1 + 11/20 n2 + 7/20 n3, where n_i denotes the number of vertices in G of degree i, for i ? {0, 1, 2, 3}. We also prove that if G is a subcubic planar graph with girth at least 9, then ?(G) < n0 + 13/17 n1 + 9/17 n2 + 6/17 n3"},{"@xml:lang":"sl","#text":"Odkar je Reed leta 1996 domneval, da je dominacijsko število povezanega kubičnega grafa reda n največ ?1/3n?, je bilo dominacijsko število kubičnih grafov obsežno preučevano. Danes je znano, da domneva na splošno ne drži, vendar sta Henning in Dorbec pokazala, da velja za grafe z ožino vsaj 9. Zhu in Wu sta podala analogno domnevo za 2-povezane kubične ravninske grafe. V tem članku podamo novo zgornjo mejo za dominacijsko število podkubičnih ravninskih grafov: če je G podkubičen ravninski graf z ožino vsaj 8, potem velja ?(G) < n0 + 3/4 n1 + 11/20 n2 + 7/20 n3, kjer n_i označuje število vozlišč v G stopnje i, za i ? {0, 1, 2, 3}. Prav tako dokažemo, da za vsak podkubičen ravninski graf G z ožino vsaj 9 velja ?(G) < n0 + 13/17 n1 + 9/17 n2 + 6/17 n3"}],"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-5M5H6R3X","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-5M5H6R3X"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-5M5H6R3X/dbb6a7bb-97e6-49b4-b97a-7611f1b03172/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-5M5H6R3X/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-5M5H6R3X"}}}}