{"?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-RKIM2139/180884a2-e201-4b2b-88e2-cd08bf33057e/PDF","dcterms:extent":"387 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-RKIM2139/af8bd699-21dd-4ad4-ba6c-1981eb79a959/TEXT","dcterms:extent":"33 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-RKIM2139","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":["Burgess, Andrea C.","Danziger, Peter","Traetta, Tommaso"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 67-78"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18912601","URN:URN:NBN:SI:doc-RKIM2139"],"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":"(generalized) Oberwolfach problem"},{"@xml:lang":"sl","#text":"(posplošeni) oberwolfaški problem"},{"@xml:lang":"en","#text":"2-factorizations"},{"@xml:lang":"sl","#text":"2-faktorizacije"},{"@xml:lang":"en","#text":"cycle systems"},{"@xml:lang":"en","#text":"Hamilton-Waterloo problem"},{"@xml:lang":"sl","#text":"hamilton-waterloojski problem"},{"@xml:lang":"en","#text":"resolvable cycle decompositions"},{"@xml:lang":"sl","#text":"rešljive dekompozicije ciklov"},{"@xml:lang":"sl","#text":"sistemi ciklov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the generalized Oberwolfach problem|"},"dc:description":[{"@xml:lang":"sl","#text":"The generalized Oberwolfach problem ?$\\rm{OP}_t(2w + 1; N_1, N_2, \\dots , Nt; \\alpha_1, \\alpha_2, \\dots, \\alpha_t)$? asks for a factorization of ?$K_{2w + 1}$? into ?$\\alpha_i C_{N_i}$?-factors (where a ?$C_{N_i}$?-factor of ?$K_{2w + 1}$? is a spanning subgraph whose components are cycles of length ?$N_i \\ge 3$?) for ?$i=1, 2, \\dots , t$?. Necessarily, ?$N=\\mathrm{lcm}(N_1, N_2, \\dots, N_t)$? is a divisor of ?$2w + 1$? and ?$w=\\sum^t_{i=1} \\alpha_i$?. For ?$t=1$? we have the classic Oberwolfach problem. For ?$t=2$? this is the well-studied Hamilton-Waterloo problem, whereas for ?$t \\ge 3$? very little is known. In this paper, we show, among other things, that the above necessary conditions are sufficient whenever ?$2w + 1 \\ge (t + 1)N$?, ?$\\alpha_i > 1$? for every ?$i \\in \\{1, 2, \\dots, t\\}$?, and ?$\\mathrm{gcd} (N_1, N_2, \\dots, N_t) > 1$?. We also provide sufficient conditions for the solvability of the generalized Oberwolfach problem over an arbitrary graph and, in particular, the complete equipartite graph"},{"@xml:lang":"sl","#text":"Pri posplošenem oberwolfaškem problemu ?$\\rm{OP}_t(2w + 1; N_1, N_2, \\dots , Nt; \\alpha_1, \\alpha_2, \\dots, \\alpha_t)$? iščemo faktorizacijo grafa ?$K_{2w + 1}$? na ?$\\alpha_i C_{N_i}$?-faktorjev (kjer je ?$C_{N_i}$?-faktor grafa ?$K_{2w + 1}$? vpeti podgraf, katerega komponente so cikli dolžine ?$N_i \\ge 3$?) za ?$i=1, 2, \\dots , t$?. Potrebni pogoj za rešitev je, da je ?$N=\\mathrm{lcm}(N_1, N_2, \\dots, N_t)$? delitelj števila ?$2w + 1$? in da je ?$ w=\\sum^t_{i=1} \\alpha_i$?. Za ?$t=1$? imamo klasični oberwolfaški problem. Za ?$t=2$? je to dobro raziskani hamilton-waterloojski problem, medtem ko je za ?$t \\ge 3$? znanega zelo malo. V tem članku med drugim pokažemo, da je zgornji potrebni pogoj tudi zadosten, kadarkoli je ?$2w + 1 \\ge (t + 1)N$?, $?\\alpha_i > 1$? za vsak ?$i \\in \\{1, 2, \\dots, t\\}$?, in ?$\\mathrm{gcd} (N_1, N_2, \\dots, N_t) > 1$?. Podamo tudi zadostne pogoje za rešljivost posplošenega oberwolfaškega problema nad poljubnim grafom in, še posebej, polnim ekvipartitnim grafom"}],"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-RKIM2139","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-RKIM2139"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-RKIM2139/180884a2-e201-4b2b-88e2-cd08bf33057e/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-RKIM2139/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-RKIM2139"}}}}