{"?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-OJ7EHEDN/6e7bb852-fcfa-4899-99a1-6864852f0d34/PDF","dcterms:extent":"317 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-OJ7EHEDN/5a79b244-c2c1-42b0-89a2-277231062555/TEXT","dcterms:extent":"23 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-OJ7EHEDN","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Barát, János","Nagy, Zoltán Lóránt"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"str. 39-47"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18701401","URN:URN:NBN:SI:doc-OJ7EHEDN"],"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":"anti-Ramsey problems"},{"@xml:lang":"sl","#text":"anti-Ramseyjevi problemi"},{"@xml:lang":"en","#text":"Latin squares"},{"@xml:lang":"sl","#text":"latinski kvadrati"},{"@xml:lang":"en","#text":"Lovász local lemma"},{"@xml:lang":"sl","#text":"Lovászeva lokalna lema"},{"@xml:lang":"en","#text":"transversals"},{"@xml:lang":"sl","#text":"transverzale"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Transversals in generalized Latin squares|"},"dc:description":[{"@xml:lang":"sl","#text":"We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order ?$n$? is equivalent to a proper edge-coloring of ?$K_{n, n}$?. A transversal corresponds to a multicolored perfect matching. S. Akbari and A. Alipour J. Comb. Des. 12, No. 5, 325-332 (2004) defined ?$l(n)$? as the least integer such that every properly edge-colored ?$K_{n, n}$?, which contains at least ?$l(n)$? different colors, admits a multicolored perfect matching. They conjectured that ?$l(n) \\leq n^2/2\\ \\mathrm{if}\\ n$? is large enough. In this note we prove that ?$l(n)$? is bounded from above by ?$0.75n^2\\ \\mathrm{if}\\ n > 1$?. We point out a connection to anti-Ramsey problems. We propose a conjecture related to a well-known result by D. E. Woolbright and H.-L. Fu J. Comb. Des. 6, No. 1, 1-20 (1998), that every proper edge-coloring of ?$K_{2n}$? admits a multicolored 1-factor"},{"@xml:lang":"sl","#text":"Iščemo zadosten pogoj za obstoj transverzale v posplošenem latinskem kvadratu. Posplošeni latinski kvadrat reda n je ekvivalenten pravilnemu barvanju povezav grafa ?$K_{n, n}$?. Transverzala ustreza večbarvnemu popolnemu prirejanju. Akbari in Alipour sta definirala ?$l(n)$? kot najmanjše celo število, za katero velja, da vsako pravilno barvanje povezav grafa ?$K_{n, n}$?, ki vsebuje najmanj ?$l(n)$? različnih barv, dopušča večbarvno popolno prirejanje. Postavila sta domnevo, da je ?$l(n) \\leq n^2/2\\ \\mathrm{if}\\ n$? če je ?$n$? dovolj velik. V tem kratkem članku dokažemo, da je število ?$l(n)$? navzgor omejeno z ?$0.75n^2\\ \\mathrm{if}\\ n > 1$?. Izpostavimo povezavo z anti-Ramseyevimi problemi. Postavimo domnevo, povezano z dobro znanim rezultatom Woolbrighta in Fuja, da vsako pravilno barvanje povezav grafa ?$K_{2n}$? dopušča večbarvni 1-faktor"}],"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-OJ7EHEDN","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-OJ7EHEDN"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-OJ7EHEDN/6e7bb852-fcfa-4899-99a1-6864852f0d34/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-OJ7EHEDN/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-OJ7EHEDN"}}}}