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Local Structure for Vertex-Minors

dc.contributor.advisorGeelen, Jim
dc.contributor.authorMcCarty, Rose
dc.date.accessioned2021-10-12T15:26:50Z
dc.date.available2021-10-12T15:26:50Z
dc.date.issued2021-10-12
dc.date.submitted2021-10-07
dc.description.abstractThis thesis is about a conjecture of Geelen on the structure of graphs with a forbidden vertex-minor; the conjecture is like the Graph Minors Structure Theorem of Robertson and Seymour but for vertex-minors instead of minors. We take a step towards proving the conjecture by determining the "local structure''. Our first main theorem is a grid theorem for vertex-minors, and our second main theorem is more like the Flat Wall Theorem of Robertson and Seymour. We believe that the results presented in this thesis provide a path towards proving the full conjecture. To make this area more accessible, we have organized the first chapter as a survey on "structure for vertex-minors''.en
dc.identifier.urihttp://hdl.handle.net/10012/17633
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectgraph theoryen
dc.subjectcombinatoricsen
dc.titleLocal Structure for Vertex-Minorsen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorGeelen, Jim
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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