dc.contributor.author Joeris, Benson dc.date.accessioned 2015-05-06 17:48:22 (GMT) dc.date.available 2015-05-06 17:48:22 (GMT) dc.date.issued 2015-05-06 dc.date.submitted 2015 dc.identifier.uri http://hdl.handle.net/10012/9315 dc.description.abstract The results in this thesis are steps toward bridging the gap between the handful of exact structure theorems known for minor-closed classes of graphs, and the very general, yet wildly qualitative, Graph Minors Structure Theorem. en This thesis introduces a refinement of the notion of tree-width. Tree-width is a measure of how “tree-like” a graph is. Essentially, a graph is tree-like if it can be decomposed across a collection of non-crossing vertex-separations into small pieces. In our variant, which we call k-tree-width, we require that the vertex-separations each have order at most k. Tree-width and branch-width are related parameters in a graph, and we introduce a branch-width-like variant for k-tree-width. We find a dual notion, in terms of tangles, for our branch-width parameter, and we prove a generalization of Robertson and Seymour’s Grid Theorem. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Graph en dc.subject K6 en dc.subject tree-decomposition en dc.subject branch-decomposition en dc.subject unavoidable-minor en dc.subject tangle en dc.subject minor en dc.title Connectivity, tree-decompositions and unavoidable-minors en dc.type Doctoral Thesis en dc.pending false dc.subject.program Combinatorics and Optimization en uws-etd.degree.department Combinatorics and Optimization en uws-etd.degree Doctor of Philosophy en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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