{"?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-2H8S7RAU/30c5d468-0adb-4ef4-b86d-5d1b2b7dc8c3/PDF","dcterms:extent":"486 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-2H8S7RAU/20761a06-b9b4-4bfe-a13a-2b95d38543e9/TEXT","dcterms:extent":"76 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-2H8S7RAU/267a05bd-8f7a-4793-ad3f-c5efbe0e8afa/PDF","dcterms:extent":"135 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-2H8S7RAU/79e2231a-cf32-468a-b11e-5e5ab52260b8/TEXT","dcterms:extent":"6 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-2H8S7RAU","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":["Di Stefano, Gabriele","Haritha, S.","Thomas, Elias John","Tuite, James","Ullas Chandran, S.V."],"dc:format":[{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"številka:4, article  p4.06"},{"@xml:lang":"sl","#text":"str. 1-27"}],"dc:identifier":["DOI:10.26493/1855-3974.3454.a3c","ISSN:1855-3974","COBISSID_HOST:294217475","URN:URN:NBN:SI:doc-2H8S7RAU"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"sl","#text":"barvanje grafov"},{"@xml:lang":"en","#text":"Cartesian product"},{"@xml:lang":"en","#text":"complexity"},{"@xml:lang":"en","#text":"general position set"},{"@xml:lang":"en","#text":"graph colouring"},{"@xml:lang":"sl","#text":"kartezični produkt"},{"@xml:lang":"sl","#text":"monofonična pozicijska množica"},{"@xml:lang":"en","#text":"monophonic position set"},{"@xml:lang":"sl","#text":"računska zahtevnost"},{"@xml:lang":"sl","#text":"splošna pozicijska množica"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Colouring a graph with position sets|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper we consider a colouring version of the general position problem. The gp-chromatic number is the smallest number of colours needed to colour V(G) such that each colour class has the no-three-in-line property. We determine bounds on this colouring number in terms of the diameter, general position number, size, chromatic number, cochromatic number and total domination number and prove realisation results. We also determine it for several graph classes, including Kneser graphs K(n,2), line graphs of complete graphs, complete multipartite graphs, block graphs and Cartesian products. We also show that the gp-colouring problem is NP-complete"},{"@xml:lang":"sl","#text":"V tem članku obravnavamo različico problema splošnega položaja, povezano z barvanjem. gp-kromatično število je najmanjše število barv, potrebnih za barvanje vozlišč grafa tako, da ima vsak barvni razred lastnost, da nobena tri njegova vozlišča ne ležijo na isti geodetski poti. Za to barvno število določimo meje v odvisnosti od premera, števila splošnega položaja, velikosti grafa, kromatičnega števila, kokromatičnega števila in totalnega dominacijskega števila ter dokažemo realizacijske rezultate. Določimo tudi gp-kromatično število za več razredov grafov, med drugim za Kneserjeve grafeK(n, 2), povezavne grafe polnih grafov, polne večdelne grafe, bločne grafe in kartezične produkte. Nazadnje pokažemo, da je problem gp-barvanja NP-poln"}],"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-2H8S7RAU","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-2H8S7RAU"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-2H8S7RAU/30c5d468-0adb-4ef4-b86d-5d1b2b7dc8c3/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-2H8S7RAU/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-2H8S7RAU"}}}}