{"?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-T4VC5H4K/a26831b3-8bb2-4bef-b1cb-d9937735e356/PDF","dcterms:extent":"375 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-T4VC5H4K/51e5d195-0089-495e-a937-9570a7ef0e4a/TEXT","dcterms:extent":"43 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-T4VC5H4K","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2025","dc:creator":["Brešar, Boštjan","Cornet, María Gracia","Dravec, Tanja","Henning, Michael A."],"dc:format":[{"@xml:lang":"sl","#text":"16 str."},{"@xml:lang":"sl","#text":"letnik:25"},{"@xml:lang":"sl","#text":"številka:4, article  p4.02"}],"dc:identifier":["DOI:10.26493/1855-3974.3294.7fd","ISSN:1855-3966","COBISSID_HOST:243733251","URN:URN:NBN:SI:doc-T4VC5H4K"],"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":"2-packing"},{"@xml:lang":"sl","#text":"2-pakiranje"},{"@xml:lang":"sl","#text":"k-dominacija"},{"@xml:lang":"en","#text":"k-domination"},{"@xml:lang":"en","#text":"Kneser graphs"},{"@xml:lang":"sl","#text":"Kneserjev graf"},{"@xml:lang":"sl","#text":"k-terna celotna dominacija"},{"@xml:lang":"en","#text":"k-tuple total domination"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"k-domination invariants on Kneser graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"In this follow-up to work of M.G. Cornet and P. Torres from 2023, where the ?$k$?-tuple domination number and the ?$2$?-packing number in Kneser graphs ?$K(n,r)$? were studied, we are concerned with two variations, the ?$k$?-domination number, ?$\\gamma_k(K(n,r))$?, and the ?$k$?-tuple total domination number, ?$\\gamma_{t\\times k}(K(n,r))$?, of ?$K(n,r)$?. For both invariants we prove monotonicity results by showing that ?$\\gamma_k(K(n,r))\\ge \\gamma_k(K(n+1,r))$? holds for any ?$n\\ge 2(k+r)$?, and ?$\\gamma_{t\\times k}(K(n,r))\\ge \\gamma_{t\\times k}(K(n+1,r))$? holds for any ?$n\\ge 2r+1$?. We prove that ?$\\gamma_k(K(n,r))=\\gamma_{t\\times k}(K(n,r))=k+r$? when ?$n\\geq r(k+r)$?, and that in this case every ?$\\gamma_k$?-set and ?$\\gamma_{t\\times k}$?-set is a clique, while ?$\\gamma_k(r(k+r)-1,r)=\\gamma_{t\\times k}(r(k+r)-1,r)=k+r+1$?, for any ?$k\\ge 2$?. Concerning the ?$2$?-packing number, ?$\\rho_2(K(n,r))$?, of ?$K(n,r)$?, we prove the exact values of ?$\\rho_2(K(3r-3,r))$? when ?$r\\ge 10$?, and give sufficient conditions for ?$\\rho_2(K(n,r))$? to be equal to some small values by imposing bounds on ?$r$? with respect to ?$n$?. We also prove a version of monotonicity for the ?$2$?-packing number of Kneser graphs"},{"@xml:lang":"sl","#text":"Članek je nadaljevanje članka M.G. Cornet, P. Torres, arXiv:2308.15603, v katerem sta avtorja raziskovala ?$k$?-terno dominacijsko število in ?$2$?-pakirno število Kneserjevih grafov ?$K(n,r)$?. Nas zanimata dve sorodni inačici, namreč ?$k$?-dominacijsko število ?$\\gamma_k(K(n,r))$? in ?$k$?-terno celotno dominacijsko število ?$\\gamma_{t\\times k}(K(n,r))$? Kneserjevih grafov ?$K(n,r)$?. Za obe invarianti dokažemo neko vrsto monotonosti in sicer, da za vse ?$n\\ge 2(k+r)$? velja ?$\\gamma_k(K(n,r))\\ge \\gamma_k(K(n+1,r))$? ter da za vse ?$n\\ge 2r+1$? velja ?$\\gamma_{t\\times k}(K(n,r))\\ge \\gamma_{t\\times k}(K(n+1,r))$?. Dokažemo tudi, da velja ?$\\gamma_k(K(n,r))=\\gamma_{t\\times k}(K(n,r))=k+r$?, če je ?$n\\geq r(k+r)$?, in da je v tem primerih vsaka ?$\\gamma_k(K(n,r))$?-množica in ?$\\gamma_{t\\times k}$?-množica klika. Po drugi strani dokažemo, da velja ?$\\gamma_k(r(k+r)-1,r)=\\gamma_{t\\times k}(r(k+r)-1,r)=k+r+1$? za vsak ?$k\\ge 2$?. Glede ?$2$?-pakirnega števila ?$\\rho_2(K(n,r))$? grafa ?$K(n,r)$? določimo točne vrednosti ?$\\rho_2(K(3r-3,r))$?, ko je ?$r\\ge 10$? in podamo zadostne pogoje v obliki mej za število ?$r$? glede na število ?$n$?, ki zagotavljajo, da je ?$\\rho_2(K(n,r))$? enako nekim predpisanim majhnim vrednostim. Dokažemo tudi neko vrsto monotonosti za ?$2$?-pakirno število Kneserjevih 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-T4VC5H4K","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-T4VC5H4K"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-T4VC5H4K/a26831b3-8bb2-4bef-b1cb-d9937735e356/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-T4VC5H4K/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-T4VC5H4K"}}}}