{"?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-GDLZJWSV/e5195816-bbd1-4ee1-89a3-59232d6e2c2c/PDF","dcterms:extent":"623 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-GDLZJWSV/01a17001-566d-46df-901b-63f09d87b1d8/TEXT","dcterms:extent":"29 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-GDLZJWSV","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Jorgensen, Leif K.","Pineda-Villavicencio, Guillermo","Ugon, Julien"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P2.09 (10 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2577.25d","COBISSID_HOST:117087235","ISSN:1855-3966","URN:URN:NBN:SI:doc-GDLZJWSV"],"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":"Cartesian product"},{"@xml:lang":"sl","#text":"ciklični politop"},{"@xml:lang":"en","#text":"connectivity"},{"@xml:lang":"en","#text":"cyclic polytope"},{"@xml:lang":"en","#text":"dual polytope"},{"@xml:lang":"sl","#text":"dualni politop"},{"@xml:lang":"sl","#text":"kartezični produkt"},{"@xml:lang":"en","#text":"k-linked"},{"@xml:lang":"sl","#text":"k-vezan"},{"@xml:lang":"en","#text":"linkedness"},{"@xml:lang":"sl","#text":"povezljivost"},{"@xml:lang":"sl","#text":"vezanost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Linkedness of Cartesian products of complete graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least ?$2k$? vertices is ?$k$?-linked if, for every set of ?$2k$? distinct vertices organised in arbitrary ?$k$? pairs of vertices, there are ?$k$? vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product ?$K^{d_1+1} \\times K^{d_2+1}$? of complete graphs ?$K^{d_1+1}$? and ?$K^{d_2+1}$? is ?$\\lfloor (d_1 + d_2)/2 \\rfloor $?-linked for ?$d_1, d_2 \\geq 2$?, and this is best possible. This result is connected to graphs of simple polytopes. The Cartesian product ?$K^{d_1+1} \\times K^{d_2+1}$? is the graph of the Cartesian product ?$T(d_1) \\times T(d_2)$? of a ?$d_1$?-dimensional simplex ?$T(d_1)$? and a ?$d_2$?-dimensional simplex ?$T(d_2)$?. And the polytope ?$T(d_1) \\times T(d_2)$? is a simple polytope, a ?$(d_1 + d_2)$?-dimensional polytope in which every vertex is incident to exactly ?$d_1 + d_2$? edges. While not every ?$d$?-polytope is ?$\\lfloor d/2 \\rfloor $?-linked, it may be conjectured that every simple ?$d$?-polytope is. Our result implies the veracity of the revised conjecture for Cartesian products of two simplices"},{"@xml:lang":"sl","#text":"Ta članek obravnava veznost kartezičnega produkta polnih grafov. Graf z najmanj ?$2k$? vozlišči je ?$k$?-vezan, če za vsako množico ?$2k$? različnih vozlišč, razvrščenih v poljubne ?$k$? pare, obstaja ?$k$? vozliščno disjunktnih poti, ki ta vozlišča povezujejo v pare. Dokažemo, da je kartezični produkt ?$K^{d_1+1} \\times K^{d_2+1}$? polnih grafov ?$K^{d_1+1}$ in $K^{d_2+1}$? ?$\\lfloor (d_1 + d_2)/2 \\rfloor $?-vezan za ?$d_1, d_2 \\geq 2$?, in da je to najboljši možni rezultat. Ta razultat je povezan z grafi enostavnih politopov. Kartezični produkt ?$K^{d_1+1} \\times K^{d_2+1}$? je graf kartezičnega produkta ?$T(d_1) \\times T(d_2)$?-dimenzionalnega simpleksa ?T$d_1$? ter ?$d_2$?-dimenzionalnega simpleksa ?$T(d_2)$?. Politop ?$T(d_1) \\times T(d_2)$? pa je enostaven politop, ?$(d_1 + d_2)$?-dimenzionalen politop, v katerem je vsaka točka incidentna natančno ?$d_1 + d_2$? povezavam. Čeprav ni vsak ?$d$?-politop ?$\\lfloor d/2 \\rfloor $?-vezan, pa lahko domnevamo, da vsak enostaven ?$d$?-politop to je. Naš rezultat implicira resničnost revidirane domneve za kartezične produkte dveh simpleksov"}],"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-GDLZJWSV","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-GDLZJWSV"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-GDLZJWSV/e5195816-bbd1-4ee1-89a3-59232d6e2c2c/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-GDLZJWSV/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-GDLZJWSV"}}}}