{"?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-Z0CK4Z6G/bc5ac1f6-913d-4fc0-aed9-8268802a1443/PDF","dcterms:extent":"437 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-Z0CK4Z6G/e1e81c7f-c91a-47a2-ac55-43f6ef6773a6/TEXT","dcterms:extent":"47 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-Z0CK4Z6G","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":["Gastineau, Nicolas","Kheddouci, Hamamache","Togni, Olivier"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 321-344"}],"dc:identifier":["COBISSID:17609561","ISSN:1855-3966","URN:URN:NBN:SI:doc-Z0CK4Z6G"],"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":"distance coloring"},{"@xml:lang":"en","#text":"hexagonal lattice"},{"@xml:lang":"en","#text":"i-packing"},{"@xml:lang":"sl","#text":"i-pakiranje"},{"@xml:lang":"sl","#text":"kvadratna mreža"},{"@xml:lang":"en","#text":"packing chromatic number"},{"@xml:lang":"sl","#text":"pakirno kromatsko število"},{"@xml:lang":"sl","#text":"razdaljno barvanje"},{"@xml:lang":"en","#text":"square lattice"},{"@xml:lang":"sl","#text":"šestkotniška mreža"},{"@xml:lang":"en","#text":"triangular lattice"},{"@xml:lang":"sl","#text":"trikotniška mreža"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Subdivision into i-packings and S-packing chromatic number of some lattices|"},"dc:description":[{"@xml:lang":"sl","#text":"An ?$i$?-packing in a graph ?$G$? is a set of vertices at pairwise distance greater than ?$i$?. For a nondecreasing sequence of integers ?$S=(s_1,s_2,\\ldots)$?, the?$S$?-packing chromatic number of a graph ?$G$? is the least integer ?$k$? such that there exists a coloring of ?$G$? into ?$k$? colors where each set of vertices colored ?$i$?, ?$i=1,\\ldots,k$?, is an ?$s_i$?-packing. This paper describes various subdivisions of an ?$i$?-packing into ?$j$?-packings ?$(j>i)$? for the hexagonal, square and triangular lattices. These results allow us to bound the ?$S$?-packing chromatic number for these graphs, with more precise bounds and exact values for sequences ?$S=(s_i,i \\in \\mathbb{N}^*)$?, ?$s_i = d+ \\lfloor (i-1)/n \\rfloor$?"},{"@xml:lang":"sl","#text":"Množici vozlišč grafa ?$G$?, paroma oddaljenih za več kot ?$i$?, pravimo ?$i$?-pakiranje. Če je ?$S=(s_1,s_2,\\ldots)$? nepadajoče zaporedje celih števil, potem je ?$S$?-pakirno kromatsko število grafa ?$G$? najmanjše celo število ?$k$?, pri katerem obstaja barvanje grafa ?$G$? s ?$k$? barvami, v katerem vsaka množica vozlišč, pobarvanih z barvo ?$i$?, ?$i=1,\\ldots,k$?, predstavlja ?$s_i$?-pakiranje. Članek opisuje različne podrazdelitve ?$i$?-pakiranj na ?$j$?-pakiranja ?$(j>i)$? za šestkotniške, kvadratne in trikotniške mreže. Ti rezultati nam omogočajo omejiti ?$S$?-pakirno kromatsko število teh grafov in določiti natančnejše meje in natančne vrednosti za zaporedja ?$S=(s_i,i \\in \\mathbb{N}^*)$?, ?$s_i = d+ \\lfloor (i-1)/n \\rfloor$?"}],"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-Z0CK4Z6G","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-Z0CK4Z6G"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-Z0CK4Z6G/bc5ac1f6-913d-4fc0-aed9-8268802a1443/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-Z0CK4Z6G/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-Z0CK4Z6G"}}}}