{"?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-4TTZIGJH/0a1d6934-02a1-4697-878b-7df67d9572e8/PDF","dcterms:extent":"413 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-4TTZIGJH/e1f1c9ef-145a-411e-8363-38b21dd4cad3/TEXT","dcterms:extent":"35 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-4TTZIGJH","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Klavžar, Sandi","Rall, Douglas F.","Yero, Ismael G."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 33-44"}],"dc:identifier":["DOI:10.26493/1855-3974.2384.77d","ISSN:1855-3966","COBISSID:72019203","URN:URN:NBN:SI:doc-4TTZIGJH"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"disociacijske množice"},{"@xml:lang":"sl","#text":"grafi"},{"@xml:lang":"sl","#text":"krepki solventni graf"},{"@xml:lang":"sl","#text":"množice"},{"@xml:lang":"sl","#text":"računska zahtevnost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"General d-position sets|"},"dc:description":[{"@xml:lang":"sl","#text":"The general ?$d$?-position number ?${\\rm gp}_d(G)$? of a graph ?$G$? is the cardinality of a largest set ?$S$? for which no three distinct vertices from ?$S$? lie on a common geodesic of length at most ?$d$?. This new graph parameter generalizes the well studied general position number. We first give some results concerning the monotonic behavior of ?${\\rm gp}_d(G)$? with respect to the suitable values of ?$d$?. We show that the decision problem concerning finding ?${\\rm gp}_d(G)$? is NP-complete for any value of ?$d$?. The value of ?${\\rm gp}_d(G)$? when ?$G$? is a path or a cycle is computed and a structural characterization of general ?$d$?-position sets is shown. Moreover, we present some relationships with other topics including strong resolving graphs and dissociation sets. We finish our exposition by proving that ?${\\rm gp}_d(G)$? is infinite whenever ?$G$? is an infinite graph and ?$d$? is a finite integer"},{"@xml:lang":"sl","#text":"Število ?$d$?-splošne lege ?${\\rm gp}_d(G)$? grafa ?$G$? je kardinalnost največje množice ?$S$?, za katero nobena trojica volišč ne leži na skupni najkrajši poti dolžine kvečjemu ?$d$?. Ta novi grafovski parameter posplošuje dobro preučeno število splošne lege. Najprej podamo nekaj rezultatov v zvezi z monotonim vedenjem ?${\\rm gp}_d(G)$? glede na primerne vrednosti ?$d$?. Pokažemo, da je odločitveni problem iskanja ?${\\rm gp}_d(G)$? NP-poln za vse ?$d$?. Izračunana je vrednost ?${\\rm gp}_d(G)$?, kadar je ?$G$? pot ali cikel, dokazana je tudi strukturna karakterizacija množic v ?$d$?-splošni legi. Poleg tega predstavljamo nekatere odnose z drugimi temami, vključno s krepkimi solventnimi grafi in disociacijskimi množicami. Našo predstavitev zaključimo z dokazom, da je ?${\\rm gp}_d(G)$? neskončno, kadar je ?$G$? neskončen graf in ?$d$? končno celo število"}],"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-4TTZIGJH","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-4TTZIGJH"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-4TTZIGJH/0a1d6934-02a1-4697-878b-7df67d9572e8/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-4TTZIGJH/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-4TTZIGJH"}}}}