{"?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-L2G170UO/0965b3cc-a95c-443d-9ec5-b2a06ac6ca29/PDF","dcterms:extent":"426 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-L2G170UO/fc8826a1-f5fb-4741-8a18-3bdfbee42378/TEXT","dcterms:extent":"46 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-L2G170UO/8018f040-420c-4ea2-8d66-8014e1da9a42/PDF","dcterms:extent":"126 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-L2G170UO/3072cf0c-3a8d-4fd4-be86-2ffb430f724c/TEXT","dcterms:extent":"4 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-L2G170UO","dcterms:issued":"2025","dc:creator":["Boruzanli Ekinci, Gülnaz","Bujtás, Csilla"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:25"},{"@xml:lang":"sl","#text":"številka:3, article  p3.07"},{"@xml:lang":"sl","#text":"str. 1-16"}],"dc:identifier":["DOI:10.26493/1855-3974.3344.4c8","ISSN:1855-3966","COBISSID:270605059","URN:URN:NBN:SI:doc-L2G170UO"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:source":{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"},"dc:subject":[{"@xml:lang":"en","#text":"bipartite Kneser graph"},{"@xml:lang":"en","#text":"covering design"},{"@xml:lang":"sl","#text":"dvodelni Kneserjev graf"},{"@xml:lang":"en","#text":"Johnson graph"},{"@xml:lang":"sl","#text":"Johnsonov graf"},{"@xml:lang":"en","#text":"Kneser graph"},{"@xml:lang":"sl","#text":"Kneserjev graf"},{"@xml:lang":"sl","#text":"množica celotne vzajemne vidnosti"},{"@xml:lang":"sl","#text":"množica vzajemne vidnosti"},{"@xml:lang":"en","#text":"mutual-visibility set"},{"@xml:lang":"sl","#text":"pokrivni načrt"},{"@xml:lang":"sl","#text":"problem Turánovega tipa"},{"@xml:lang":"en","#text":"total mutual-visibility set"},{"@xml:lang":"en","#text":"Turán-type problem"}],"dc:title":{"@xml:lang":"sl","#text":"Mutual-visibility problems in Kneser and Johnson graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G$? be a connected graph and ?$X \\subseteq V(G)$?. By definition, two vertices ?$u$? and ?$v$? are ?$X$?-visible in ?$G$? if there exists a shortest ?$u, v$?-path with all internal vertices being outside of the set ?$X$?. The largest size of ?$X$? such that any two vertices of ?$G$? (resp. any two vertices from ?$X$?) are ?$X$?-visible is the total mutual-visibility number (resp. the mutual-visibility number) of ?$G$?. In this paper, we determine the total mutual-visibility number of Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The formulas proved for Kneser, and bipartite Kneser graphs are related to the size of transversal-critical uniform hypergraphs, while the total mutual-visibility number of Johnson graphs is equal to a hypergraph Turán number. Exact values or estimates for the mutual-visibility number over these graph classes are also established"},{"@xml:lang":"sl","#text":"Naj bo ?$G$? povezan graf in ?$X \\subseteq V(G)$?. Vozlišči ?$u$? in ?$v$? v ?$G$? sta ?$X$?-vidni, če obstaja najkrajša ?$u,v$?-pot, pri kateri so vsa notranja vozlišča zunaj množice ?$X$?. Največja velikost ?$X$?, tako da sta kateri koli dve vozlišči ?$G$? (oziroma kateri koli dve vozlišči iz ?$X$?) ?$X$?-vidni, je število celotne vzajemne vidnosti (oziroma število vzajemne vidnosti) ?$G$?. V tem članku določimo število celotve vzajemne vidnosti Kneserjevih grafov, dvodelnih Kneserjevih grafov in Johnsonovih grafov. Formule, dokazane za Kneserjeve in dvodelne Kneserjeve grafe, so povezane z velikostjo transverzalno kritičnih uniformnih hipergrafov, medtem ko je število celotne vzajemne vidnosti Johnsonovih grafov enako Turánovemu številu hipergrafa. Določene so tudi natančne vrednosti ali ocene za število vzajemne vidnosti za te razrede grafov"}],"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-L2G170UO","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-L2G170UO"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-L2G170UO/0965b3cc-a95c-443d-9ec5-b2a06ac6ca29/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-L2G170UO/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-L2G170UO"}}}}