{"?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-VTEH5KLN/8bea224f-56c6-4749-a583-765275ed6e44/PDF","dcterms:extent":"304 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-VTEH5KLN/42ebf95d-4e2d-4a86-8a68-80c20b0ed893/TEXT","dcterms:extent":"18 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-VTEH5KLN","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":["Chen, Fuyuan","Ning, Bo"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"str. 91-98"}],"dc:identifier":["COBISSID:17734233","ISSN:1855-3966","URN:URN:NBN:SI:doc-VTEH5KLN"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"celoštevilski tok"},{"@xml:lang":"sl","#text":"nikjer-ničeln 3-tok"},{"@xml:lang":"sl","#text":"orientacija po modulu 3"},{"@xml:lang":"sl","#text":"povezavni rezi"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A note on nowhere-zero 3-flows and Zsub3-connectivity|"},"dc:description":[{"@xml:lang":"sl","#text":"There are many major open problems in integer flow theory, such as Tutte's 3-flow conjecture that every 4-edge-connected graph admits a nowhere-zero 3-flow, Jaeger et al.'s J. Comb. Theory, Ser. B 56, No. 2, 165--182 (1992) conjecture that every 5-edge-connected graph is ?$Z_3$?-connected and Kochol's J. Comb. Theory, Ser. B 83, No. 2, 258--261 (2001) conjecture that every bridgeless graph with at most three 3-edge-cuts admits a nowhere-zero 3-flow (an equivalent version of 3-flow conjecture). C. Thomassen J. Comb. Theory, Ser. B 102, No. 2, 521--529 (2012) proved that every 8-edge-connected graph is ?$Z_3$?-connected and therefore admits a nowhere-zero 3-flow. Furthermore, Lovász et al. J. Comb. Theory, Ser. B 103, No. 5, 587--598 (2013) improved Thomassen's result to 6-edge-connected graphs. In this paper, we prove that: (1) Every 4-edge-connected graph with at most seven 5-edge-cuts admits a nowhere-zero 3-flow. (2) Every bridgeless graph containing no 5-edge-cuts but at most three 3-edge-cuts admits a nowhere-zero 3-flow. (3) Every 5-edge-connected graph with at most five 5-edge-cuts is ?$Z_3$?-connected. Our main theorems are partial results to Tutte's 3-flow conjecture, Kochol's conjecture and Jaeger et al.'s conjecture, respectively"},{"@xml:lang":"sl","#text":"V teoriji celoštevilskih tokov je veliko odprtih problemov, kot so Tuttejeva domneva o 3-toku, po kateri vsak 4-povezavno-povezan graph dopušča nikjer-ničeln 3-tok, domneva Jaegerja in soavtorjev, da je vsak 5-povezavnopovezan graf ?$Z_3$?-povezan, in Kocholova domneva, da vsak brezmostni graf z največ tremi 3-povezavnimi-rezi dopušča nikjer-ničelni 3-tok (ekvivalentna različica domneve o 3-toku). Thomassen je dokazal, da je vsak 8-povezavno-povezan graf ?$Z_3$?-povezan in da zato dopušča nikjer-ničeln 3-tok. Nadalje so Lovasz, Thomassen, Wu in Zhang izboljšali Thomassenov rezultat na 6-povezavno-povezane grafe. V članku dokažemo, da: (1) Vsak 4-povezavno-povezan graf z največ sedmimi 5-povezavnimi-rezi dopušča nikjer-ničelni 3-tok. (2) Vsak brezmostni graf, ki ne vsebuje nobenih 5-povezavnihrezov, vsebuje pa največ tri 3-povezavne-reze dopušča nikjerničelni 3-tok. (3) Vsak 5-povezavno-povezani graf z največ petimi 5-povezavnimi-rezi je ?$Z_3$?-povezan. Naši glavni izreki predstavljajo delne rezultate za Tuttejevo domnevo o 3-toku, za Kocholovo domnevo ter za domnevo Jaegerja in soavtorjev"}],"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-VTEH5KLN","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-VTEH5KLN"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-VTEH5KLN/8bea224f-56c6-4749-a583-765275ed6e44/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-VTEH5KLN/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-VTEH5KLN"}}}}