{"?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-0Q2QC4LR/ee7023d1-8f2c-4f4d-9c91-4fb7825f3a0b/PDF","dcterms:extent":"292 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-0Q2QC4LR/bf7a27a9-4fbc-4357-8e07-6800832babd5/TEXT","dcterms:extent":"19 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-0Q2QC4LR","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":"Patkós, Balázs","dc:format":[{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 273-280"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:41154563","URN:URN:NBN:SI:doc-0Q2QC4LR"],"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":"general position problem"},{"@xml:lang":"en","#text":"intersection theorems"},{"@xml:lang":"en","#text":"Kneser graphs"},{"@xml:lang":"sl","#text":"Kneserjevi grafi"},{"@xml:lang":"sl","#text":"presečni izreki"},{"@xml:lang":"sl","#text":"problem splošne lege"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the general position problem on Kneser graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"In a graph ?$G$?, a geodesic between two vertices ?$x$? and ?$x$? is a shortest path connecting ?$x$? to ?$y$?. A subset ?$S$? of the vertices of ?$G$? is in general position if no vertex of ?$S$? lies on any geodesic between two other vertices of ?$S$?. The size of a largest set of vertices in general position is the general position number that we denote by ?$gp(G)$?. Recently, Ghorbani et al, proved that for any ?$k$? if ?$n\\ge k^3-k^2+2k-2$?, then ?$gp(Kn_{n,k})=\\binom{n-1}{k-1}$?, where ?$Kn_{n,k}$? denotes the Kneser graph. We improve on their result and show that the same conclusion holds for ?$n\\ge 2.5k-0.5$? and this bound is best possible. Our main tools are a result on cross-intersecting families and a slight generalization of Bollobás's inequality on intersecting set pair systems"},{"@xml:lang":"sl","#text":"Geodetka v grafu ?$G$? med točkama ?$x$? in ?$x$? je najkrajša pot, ki povezuje ?$x$? z ?$x$?. Podmnožica ?$S$? točk grafa ?$G$? je v splošni legi, če nobena točka množice ?$S$? ne leži na nobeni geodetki med dvema drugima točkama množice ?$S$?. Velikost največje množice točk v splošni legi imenujemo splošnoležnost in označimo z ?$gp(G)$?. Nedavno so Ghorbani in dr. dokazali, da za vsak ?$k$?, ki ustreza pogoju ?$n\\ge k^3-k^2+2k-2$?, velja ?$gp(Kn_{n,k})=\\binom{n-1}{k-1}$, kjer $Kn_{n,k}$? označuje Kneserjev graf. V članku izboljšamo njihov rezultat in dokažemo, da velja isti zaključek ob predpostavki ?$n\\ge 2.5k-0.5$?, in da je ta meja najboljša možna. Naši glavni orodji sta rezultat o križno sekajočih se družinah in rahla posplošitev Bollobásove neenakosti o presečni množici parnih sistemov"}],"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-0Q2QC4LR","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-0Q2QC4LR"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-0Q2QC4LR/ee7023d1-8f2c-4f4d-9c91-4fb7825f3a0b/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-0Q2QC4LR/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-0Q2QC4LR"}}}}