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On the fine structure of graphs avoiding certain complete bipartite minors

dc.creatorSolava, Ryan William
dc.date.accessioned2020-08-22T20:48:54Z
dc.date.available2019-08-19
dc.date.issued2019-08-19
dc.identifier.urietd-08182019-190904
dc.identifier.urihttp://hdl.handle.net/1803/13941
dc.description.abstractAvoiding complete bipartite graphs as minors, and in particular $K_{2,t}$ as a minor, has been used to give sufficient conditions for Hamiltonicity. For this reason and others, the classes of $K_{2,t}$-minor-free graphs are of interest. Ding gave a rough description of the $K_{2,t}$-minor-free graphs that gives necessary conditions for a graph to be $K_{2,t}$-minor-free. We refine this description and characterize the $K_{2,t}$-minor-free graphs in the 3- and 4-connected cases, giving necessary and sufficient conditions. We also give a program for characterizing the 3-connected $K_{2,5}$-minor-free graphs. As part of this program, we prove a result on fan expansions that is of independent interest.
dc.format.mimetypeapplication/pdf
dc.subjectGraph theory
dc.subjectGraph minors
dc.titleOn the fine structure of graphs avoiding certain complete bipartite minors
dc.typedissertation
dc.contributor.committeeMemberAkram Aldroubi
dc.contributor.committeeMemberPaul Edelman
dc.contributor.committeeMemberMichael Mihalik
dc.contributor.committeeMemberJerry Spinrad
dc.type.materialtext
thesis.degree.namePHD
thesis.degree.leveldissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorVanderbilt University
local.embargo.terms2019-08-19
local.embargo.lift2019-08-19
dc.contributor.committeeChairMark Ellingham


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