{"?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-APWJZCSB/a125289f-eeee-401f-ac7c-8f77a35c7fea/PDF","dcterms:extent":"314 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-APWJZCSB/dc80c949-fc52-4ec9-91d5-2474df3c6109/TEXT","dcterms:extent":"21 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-APWJZCSB","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2014","dc:creator":["Korže, Danilo","Vesel, Aleksander"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:7"},{"@xml:lang":"sl","#text":"str. 13-22"}],"dc:identifier":["COBISSID:17063446","ISSN:1855-3966","URN:URN:NBN:SI:doc-APWJZCSB"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"computer search"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"en","#text":"hexagonal lattice"},{"@xml:lang":"en","#text":"packing chromatic number"},{"@xml:lang":"en","#text":"square lattice"},{"@xml:lang":"sl","#text":"teorija grafov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the packing chromatic number of square and hexagonal lattice|"},"dc:description":{"@xml:lang":"sl","#text":"The packing chromatic number ?$\\chi_p(G)$? of a graph ?$G$? is the smallest integer ?$k$? such that the vertex set ?$V(G)$? can be partitioned into disjoint classes? $X_1, \\dots , X_k$?, with the condition that vertices in ?$X_i$? have pairwise distance greater than ?$i$?. We show that the packing chromatic number for the hexagonal lattice ?$\\mathcal{H}$? is 7. We also investigate the packing chromatic number for infinite subgraphs of the square lattice ?$\\mathbb{Z}^2$? with up to 13 rows. In particular, we establish the packing chromatic number for ?$P_6 \\Box \\mathbb{Z}$? and provide new upper bounds on these numbers for the other subgraphs of interest. Finally, we explore the packing chromatic number for some infinite subgraphs of ?$\\mathbb{Z}^2 \\Box P_2$?. The results are partially obtained by a computer search"},"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-APWJZCSB","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-APWJZCSB"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-APWJZCSB/a125289f-eeee-401f-ac7c-8f77a35c7fea/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-APWJZCSB/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-APWJZCSB"}}}}