Flows in signed graphs with two negative edges

dc.contributor.authorRollová, Edita
dc.contributor.authorSchubert, Michael
dc.contributor.authorSteffen, Eckhard
dc.date.accessioned2022-02-28T11:00:28Z
dc.date.available2022-02-28T11:00:28Z
dc.date.issued2018
dc.description.abstract-translatedThe presented paper studies the flow number F(G, σ) of flow-admissible signed graphs (G, σ) with two negative edges. We restrict our study to cubic graphs, because for each non-cubic signed graph (G, σ) there is a set of cubic graphs obtained from (G, σ) such that the flow number of (G, σ) does not exceed the flow number of any of the cubic graphs. We prove that F(G, σ) 6 6 if (G, σ) contains a bridge, and F(G, σ) 6 7 in general. We prove better bounds, if there is a cubic graph (H, σH) obtained from (G, σ) which satisfies some additional conditions. In particular, if H is bipartite, then F(G, σ) 6 4 and the bound is tight. If H is 3-edge-colorable or critical or if it has a sufficient cyclic edge-connectivity, then F(G, σ) 6 6. Furthermore, if Tutte’s 5-Flow Conjecture is true, then (G, σ) admits a nowhere-zero 6-flow endowed with some strong properties.en
dc.format18 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationROLLOVÁ, E. SCHUBERT, M. STEFFEN, E. Flows in signed graphs with two negative edges. Electronic Journal of Combinatorics, 2018, roč. 25, č. 2, s. 1-18. ISSN: 1077-8926cs
dc.identifier.document-number440230000006
dc.identifier.doi10.37236/4458
dc.identifier.issn1077-8926
dc.identifier.obd43935089
dc.identifier.uri2-s2.0-85048345743
dc.identifier.urihttp://hdl.handle.net/11025/47056
dc.language.isoenen
dc.project.IDGA17-04611S/Ramseyovské aspekty barvení grafůcs
dc.project.IDLO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnostcs
dc.project.IDGA14-19503S/Barevnost a struktura grafůcs
dc.publisherAustralian National Universityen
dc.relation.ispartofseriesElectronic Journal of Combinatoricsen
dc.rights© authoren
dc.rights.accessopenAccessen
dc.subject.translatedflowsen
dc.subject.translatedsigned graphsen
dc.subject.translatednegative edgesen
dc.titleFlows in signed graphs with two negative edgesen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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