{"?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-J84G2CVZ/aabc1904-d483-4464-897e-12bd96c4c4d9/PDF","dcterms:extent":"224 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-J84G2CVZ/1244453e-80cf-4d7b-a6ff-542af44b2009/TEXT","dcterms:extent":"8 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-J84G2CVZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Lužar, Borut","Škrekovski, Riste"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 291-295"}],"dc:identifier":["COBISSID:17229401","ISSN:1855-3966","URN:URN:NBN:SI:doc-J84G2CVZ"],"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":"injective coloring"},{"@xml:lang":"sl","#text":"injektivno barvanje"},{"@xml:lang":"en","#text":"planar graph"},{"@xml:lang":"sl","#text":"ravninski grafi"},{"@xml:lang":"sl","#text":"teorija grafov"},{"@xml:lang":"sl","#text":"Wegnerjeva hipoteza"},{"@xml:lang":"en","#text":"Wegner's conjecture"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Counterexamples to a conjecture on injective colorings|"},"dc:description":[{"@xml:lang":"sl","#text":"An injective coloring of a graph is a vertex coloring where two vertices receive distinct colors if they have a common neighbor. Chen, Hahn, Raspaud, and Wang Some results on the injective chromatic number of graphs, J. Comb. Optim. 24 (2012), 299-318. conjectured that every planar graph with maximum degree ?$\\Delta \\ge 3$? admits an injective coloring with at most ?$\\lceil 3\\Delta / 2 \\rceil$? colors. We present an infinite family of planar graphs showing that the conjecture is false for graphs with small or even maximum degree. We conclude this note with an alternative conjecture, which sheds some light on the well-known Wegner's conjecture for the mentioned degrees"},{"@xml:lang":"sl","#text":"Injektivno barvanje grafov je barvanje vozlišč, pri katerem dve vozlišči prejmeta različni barvi, če imata skupnega soseda. Chen, Hahn, Raspaud in Wang so postavili hipotezo, da za vsak ravninski graf z maksimalno stopnjo ?$\\Delta \\ge 3$? obstaja injektivno barvanje s kvečjemu ?$\\lceil 3\\Delta/2 \\rceil$? barvami. Predstavimo neskončno družino ravninskih grafov z majhno ali sodo maksimalno stopnjo, za katere hipoteza ne drži. Članek zaključimo z alternativno domnevo, ki rahlo spominja na Wegnerjevo conjecture za omenjene stopnje"}],"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-J84G2CVZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-J84G2CVZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-J84G2CVZ/aabc1904-d483-4464-897e-12bd96c4c4d9/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-J84G2CVZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-J84G2CVZ"}}}}