{"?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-PQ3QJVUG/43fe81d2-c98f-49e6-b545-1b9617de9800/PDF","dcterms:extent":"379 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-PQ3QJVUG/3326b5cf-c982-4829-8f8a-bf631a2425b9/TEXT","dcterms:extent":"22 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-PQ3QJVUG","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":["Keranen, Melissa S.","Pastine, Adrián"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 525-533"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18963801","URN:URN:NBN:SI:doc-PQ3QJVUG"],"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-factorizations"},{"@xml:lang":"sl","#text":"2-faktorizacija"},{"@xml:lang":"sl","#text":"ciklična dekompozicija"},{"@xml:lang":"en","#text":"cycle decomposition"},{"@xml:lang":"sl","#text":"hamiltonsko-waterloojski problem"},{"@xml:lang":"en","#text":"Hamilton-Waterloo problem"},{"@xml:lang":"en","#text":"Oberwolfach problem"},{"@xml:lang":"sl","#text":"oberwolfaški problem"},{"@xml:lang":"en","#text":"resolvable decompositions"},{"@xml:lang":"sl","#text":"rešljiva dekompozicija"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity|"},"dc:description":[{"@xml:lang":"sl","#text":"The Hamilton-Waterloo problem asks for a decomposition of the complete graph of order ?$v$? into ?$r?$ copies of a 2-factor ?$F_1$? and ?$s$? copies of a 2-factor ?$F_2$? such that ?$r +s = \\lfloor\\frac{ (v - 1)}{2} \\rfloor $?. If ?$F_1$? consists of ?$m$?-cycles and ?$F_2$? consists of ?$n$? cycles, we say that a solution to ?$(m, n)- \\text{HWP}(v; r, s)$? exists. The goal is to find a decomposition for every possible pair ?$(r, s)$?. In this paper, we show that for odd ?$x$? and ?$y$?, there is a solution to ?$(2^kx, y) -\\text{HWP}(vm; r, s)$? if ?$\\gcd (x, y) \\geq 3$?, ?$m\\geq 3$?, and both ?$x$? and ?$y$? divide ?$v$?, except possibly when ?$1 \\in \\{r, s\\}$?"},{"@xml:lang":"sl","#text":"Hamiltonsko-waterloojski problem sprašuje po dekompoziciji polnega grafa reda ?$v$? na ?$r$? kopij 2-faktorja ?$F_1$? in s kopij 2-faktorja ?$F_2$?, pri čemer je ?$r +s = \\lfloor\\frac{ (v - 1)}{2} \\rfloor $?. Če ?$F_1$? sestoji iz ?$m$?-ciklov in ?$F_2$? sestoji iz ?$n$? ciklov, pravimo, da rešitev za ?$(m, n)- \\text{HWP}(v; r, s)$? obstaja. Cilj je najti dekompozicijo za vsak možen par ?$(r, s)$?. V članku pokažemo, da za liha ?$x$? in ?$y$? obstaja rešitev za ?$(2^kx, y) -\\text{HWP}(vm; r, s)$?, če je ?$\\gcd (x, y) \\geq 3$?, ?$m\\geq 3$? in tako ?$x$? kot ?$y$? delita ?$v$?, razen morda, ko je ?$1 \\in \\{r, s\\}$?"}],"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-PQ3QJVUG","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-PQ3QJVUG"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-PQ3QJVUG/43fe81d2-c98f-49e6-b545-1b9617de9800/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-PQ3QJVUG/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-PQ3QJVUG"}}}}