{"?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-050QJIMQ/d0be6a99-a191-4dd5-80ed-7b4b0e9ea38e/PDF","dcterms:extent":"293 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-050QJIMQ/a8bddfc9-6222-4116-a460-cb7463ac25d9/TEXT","dcterms:extent":"33 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-050QJIMQ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":["Furmańczyk, Hanna","Kubale, Marek"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 333-347"}],"dc:identifier":["COBISSID:17834585","ISSN:1855-3966","URN:URN:NBN:SI:doc-050QJIMQ"],"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":"corona graph"},{"@xml:lang":"en","#text":"cubic graph"},{"@xml:lang":"en","#text":"equitable chromatic number"},{"@xml:lang":"en","#text":"equitable graph coloring"},{"@xml:lang":"sl","#text":"kronski graf"},{"@xml:lang":"sl","#text":"kubični graf"},{"@xml:lang":"sl","#text":"nepristransko barvanje"},{"@xml:lang":"sl","#text":"nepristransko kromatsko število"},{"@xml:lang":"en","#text":"NP-hardness"},{"@xml:lang":"sl","#text":"NP-težko"},{"@xml:lang":"sl","#text":"polinomski algoritem"},{"@xml:lang":"en","#text":"polynomial algorithm"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Equitable coloring of corona products of cubic graphs is harder than ordinary coloring|"},"dc:description":[{"@xml:lang":"sl","#text":"A graph is equitably $k$-colorable if its vertices can be partitioned into ?$k$? independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest ?$k$? for which such a coloring exists is known as the equitable chromatic number of ?$G$? and it is denoted by ?$\\chi_=(G)$?. In this paper the problem of determinig ?$\\chi_ =$? for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas of cubic graphs is solvable in polynomial time, the problem of equitable coloring becomes NP-hard for these graphs. We provide polynomially solvable cases of coronas of cubic graphs and prove the NP-hardness in a general case. As a by-product we obtain a simple linear time algorithm for equitable coloring of such graphs which uses ?$\\chi_=(G)$? or ?$\\chi_=(G)+1$? colors. Our algorithm is best possible, unless P=NP. Consequently, cubical coronas seem to be the only known class of graphs for which equitable coloring is harder than ordinary coloring"},{"@xml:lang":"sl","#text":"Graf se imenuje nepristransko ?$k$?-obarvljiv, če lahko njegova vozlišča razvrstimo v ?$k$? neodvisnih množic na tak način, da se število vozlišč v poljubnih dveh množicah razlikuje za največ ena. Najmanjši ?$k$?, za katerega obstaja takšno barvanje, je znan kot nepristransko kromatsko število grafa ?$G$? in ga označimo ?$\\chi_=(G)$?. V tem članku študiramo problem določitve ?$\\chi_ =$? za krone kubičnih grafov. Čeprav je problem navadnega barvanja kron kubičnih grafov rešljiv v polinomskem času, je problem nepristranskega barvanja za te grafe NP-težak. Prikažemo polinomsko rešljive primere kron kubičnih grafov in dokažemo NP-težavnost v splošnem primeru. Kot stranski produkt dobimo preprost algoritem z linearno časovno zahtevnostjo za nepristransko barvanje takšnih grafov, ki uporabi ?$\\chi_=(G)$? ali ?$\\chi_=(G)+1$? barv. Naš algoritem je najboljši možen, razen če P=NP. Posledično, kubični kronski grafi se zdijo edini znani razred grafov, za katere je nepristransko barvanje težje kot običajno barvanje"}],"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-050QJIMQ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-050QJIMQ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-050QJIMQ/d0be6a99-a191-4dd5-80ed-7b4b0e9ea38e/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-050QJIMQ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-050QJIMQ"}}}}