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dc.contributor.authorHwang, Steven
dc.date.accessioned2022-12-23 14:47:13 (GMT)
dc.date.available2022-12-23 14:47:13 (GMT)
dc.date.issued2022-12-23
dc.date.submitted2022-12-21
dc.identifier.urihttp://hdl.handle.net/10012/19001
dc.description.abstractGiven a directed graph, a directed cut is a cut with all arcs oriented in the same direction, and a directed join is a set of arcs which intersects every directed cut at least once. Edmonds and Giles conjectured for all weighted directed graphs, the minimum weight of a directed cut is equal to the maximum size of a packing of directed joins. Unfortunately, the conjecture is false; a counterexample was first given by Schrijver. However its ”dual” statement, that the minimum weight of a dijoin is equal to the maximum number of dicuts in a packing, was shown to be true by Luchessi and Younger. Various relaxations of the conjecture have been considered; Woodall’s conjecture remains open, which asks the same question for unweighted directed graphs, and Edmond- Giles conjecture was shown to be true in the special case of source-sink connected directed graphs. Following these inquries, this thesis explores different relaxations of the Edmond- Giles conjecture.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectpackingen
dc.subjectcoveringen
dc.subjectdijoinsen
dc.titleThe Edmonds-Giles Conjecture and its Relaxationsen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws-etd.embargo.terms0en
uws.contributor.advisorGuenin, Bertrand
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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