{"?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-5EXVXLEW/8FEA36AA-636F-497D-9DA5-06C4C18A6764/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5EXVXLEW/06f30901-1738-4548-9584-a4a10607ac14/PDF","dcterms:extent":"300 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5EXVXLEW/a7acf488-f63c-462f-a200-4ab8b2d5d6f1/TEXT","dcterms:extent":"24 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-5EXVXLEW","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2013","dc:creator":"Milanič, Martin","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:6"},{"@xml:lang":"sl","#text":"str. 89-97"}],"dc:identifier":["COBISSID:1024423764","ISSN:1855-3966","URN:URN:NBN:SI:doc-5EXVXLEW"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"domination number"},{"@xml:lang":"en","#text":"hereditary graph class"},{"@xml:lang":"en","#text":"IDD-perfect graph"},{"@xml:lang":"en","#text":"independence-domination number"},{"@xml:lang":"en","#text":"NP-completeness"},{"@xml:lang":"en","#text":"Vizing's conjecture"},{"@xml:lang":"en","#text":"weakly chordal graph"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A note on domination and independence-domination numbers of graphs|"},"dc:description":{"@xml:lang":"sl","#text":"Vizing's conjecture is true for graphs ?$G$? satisfying ?$\\gamma^i(G) = \\gamma(G)$?, where ?$\\gamma(G)$? is the domination number of a graph ?$G$? and ?$\\gamma^i(G)$? is the independence-domination number of ?$G$?, that is, the maximum, over all independent sets ?$I$? in ?$G$?, of the minimum number of vertices needed to dominate ?$I$?. The equality ?$\\gamma^i(G) = \\gamma(G)$? is known to hold for all chordal graphs and for chordless cycles of length ?$0 \\pmod{3}$?. We prove some results related to graphs for which the above equality holds. More specifically, we show that the problems of determining whether ?$\\gamma^i(G) = \\gamma(G) = 2$? and of verifying whether ?$\\gamma^i(G) \\ge 2$? are NP-complete, even if ?$G$? is weakly chordal. We also initiate the study of the equality ?$\\gamma^i = \\gamma$? in the context of hereditary graph classes and exhibit two infinite families of graphs for which ?$\\gamma^i < \\gamma$?"},"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-5EXVXLEW","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-5EXVXLEW"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-5EXVXLEW/8FEA36AA-636F-497D-9DA5-06C4C18A6764/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-5EXVXLEW/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-5EXVXLEW"}}}}