{"?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-WA2P4H1M/43828506-c7b6-409a-bce0-cff8d12fe72d/PDF","dcterms:extent":"812 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-WA2P4H1M/256d1e8c-17a9-4fa0-84ab-3b6e9857e71b/TEXT","dcterms:extent":"29 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-WA2P4H1M/d0a64a11-ec45-4cf0-9f50-ba3fadbc76ff/PDF","dcterms:extent":"214 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-WA2P4H1M/eefdf997-082c-42be-96fb-02888b660e52/TEXT","dcterms:extent":"4 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-WA2P4H1M","dcterms:issued":"2025","dc:creator":["Klavžar, Sandi","Manuel, Paul","Prabha, R."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1 article  p1.02"},{"@xml:lang":"sl","#text":"12 str."},{"@xml:lang":"sl","#text":"letnik:8"}],"dc:identifier":["DOI:10.26493/2590-9770.1745.5f4","COBISSID_HOST:226849283","ISSN:2590-9770","URN:URN:NBN:SI:doc-WA2P4H1M"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:source":{"@xml:lang":"sl","#text":"The art of discrete and applied mathematics"},"dc:subject":[{"@xml:lang":"en","#text":"Benes network"},{"@xml:lang":"sl","#text":"Benešovo omrežje"},{"@xml:lang":"en","#text":"edge geodesic cover problem"},{"@xml:lang":"en","#text":"edge k-general position problem"},{"@xml:lang":"en","#text":"general position set"},{"@xml:lang":"sl","#text":"hiperkocke"},{"@xml:lang":"en","#text":"hypercubes"},{"@xml:lang":"sl","#text":"množica v splošni legi"},{"@xml:lang":"sl","#text":"problem geodetskega pokritja povezav"},{"@xml:lang":"sl","#text":"problem k-splošne lege za povezave"},{"@xml:lang":"en","#text":"torus network"},{"@xml:lang":"sl","#text":"torusni graf"}],"dc:title":{"@xml:lang":"sl","#text":"Generalization of edge general position problem|"},"dc:description":[{"@xml:lang":"sl","#text":"The edge geodesic cover problem of a graph ?$G$? is to find a smallest number of geodesics that cover the edge set of ?$G$?. The edge ?$k$?-general position problem is introduced as the problem to find a largest set ?$S$? of edges of ?$G$? such that at most ?$k-1$? edges of ?$S$? lie ona common geodesic. We show that these are dual min-max problems and connect them to an edge geodesic partition problem. Using these connections, exact values of the edge ?$k$?-general position number is determined for different values of ?$k$? and for various networks including torus networks, hypercubes, and Benes networks"},{"@xml:lang":"sl","#text":"Problem geodetskega pokritja povezav grafa ?$G$? je poiskati najmanjše število najkrajših poti, ki pokrivajo množico povezav grafa ?$G$?. Problem ?$k$?-splošne lege za povezave je uveden kot problem iskanja največje množice ?$S$? povezav grafa ?$G$?, tako da največ ?$k-1$? povezav iz ?$S$? leži na skupni najkrajši poti. Pokažemo, da sta to dualna min-max problema, in ju povežemo s problemom povezavne geodetske razdelitve. S temi zvezami določimo natančne vrednosti števila ?$k$?-splošne lege za povezave za različne vrednosti ?$k$? in za različna omrežja, vključno s torusnimi grafi, hiperkockami in Benešovimi omrežji"}],"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-WA2P4H1M","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-WA2P4H1M"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-WA2P4H1M/43828506-c7b6-409a-bce0-cff8d12fe72d/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/page/InC/1.0/"},"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-WA2P4H1M/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-WA2P4H1M"}}}}