{"?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-XE8D238I/2d598581-8a67-465b-8c3d-9c0127304b15/PDF","dcterms:extent":"412 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-XE8D238I/3121b180-9a34-41bc-aa62-5028c4317e0c/TEXT","dcterms:extent":"51 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-XE8D238I/7c337791-b44c-499e-9093-6238ede75e44/PDF","dcterms:extent":"124 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-XE8D238I/47de9e81-f1a3-4a90-b8e6-d74bb526b151/TEXT","dcterms:extent":"4 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-XE8D238I","dcterms:issued":"2026","dc:creator":["Máčajová, Edita","Mazzuoccolo, Giuseppe","Tabarelli, Gloria"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.03"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-22"}],"dc:identifier":["DOI:10.26493/1855-3974.3409.c13","ISSN:1855-3974","COBISSID_HOST:289253891","URN:URN:NBN:SI:doc-XE8D238I"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:source":{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"},"dc:subject":[{"@xml:lang":"en","#text":"Berge-Fulkerson conjecture"},{"@xml:lang":"sl","#text":"Berge-Fulkersonova domneva"},{"@xml:lang":"sl","#text":"ciklična povezanost"},{"@xml:lang":"en","#text":"cycle double cover"},{"@xml:lang":"en","#text":"cyclic connectivity"},{"@xml:lang":"sl","#text":"krov dvojih ciklov"},{"@xml:lang":"sl","#text":"snark"}],"dc:title":{"@xml:lang":"sl","#text":"Cycle separating cuts in possible counterexamples to the cycle double cover and the Berge-Fulkerson conjectures|"},"dc:description":[{"@xml:lang":"sl","#text":"It is known that smallest counterexamples to the Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture (if they exist) are cyclically 4- and 5-edge-connected, respectively. We further analyse small cycle separating cuts in possible counterexamples. We prove that if a smallest counterexample G to the CDC Conjecture contains a cycle separating 4-cut S, then the behaviour of the admissible CDC coverings along the dangling edges of the two 4-poles induced by S is uniquely determined among more than 2 a priori possibilities. Similarly, for the Berge-Fulkerson Conjecture, we prove that among more than 2 a priori possibilities, there are only 13 pairs of admissible sets that could occur along the dangling edges of a 5-cut in a smallest counterexample"},{"@xml:lang":"sl","#text":"Znano je, da so najmanjši protiprimeri k domnevi o krovih dvojih ciklov (Cycle Double Cover Conjecture) in k Berge–Fulkersonovi domnevi (če obstajajo) ciklično 4- oziroma 5-povezavno-povezani. Nadalje analiziramo majhne cikel-seperacijske reze v možnih protiprimerih. Dokažemo, da če najmanjši protiprimer G k domnevi CDC vsebuje cikel-seperacijski 4-rez S, je vedenje dopustnih CDC-pokritij vzdolž visečih robov obeh 4-polov, ki ju inducira S, enolično določeno med več kot 2 a priori možnostmi. Podobno za Berge–Fulkersonovo domnevo dokažemo, da je med več kot 2 a priori možnostmi le 13 parov dopustnih množic, ki bi se lahko pojavili vzdolž visečih robov 5-reza v najmanjšem protiprimeru"}],"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-XE8D238I","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-XE8D238I"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-XE8D238I/2d598581-8a67-465b-8c3d-9c0127304b15/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-XE8D238I/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-XE8D238I"}}}}