dc.creator | Solava, Ryan William | |
dc.date.accessioned | 2020-08-22T20:48:54Z | |
dc.date.available | 2019-08-19 | |
dc.date.issued | 2019-08-19 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-08182019-190904 | |
dc.identifier.uri | http://hdl.handle.net/1803/13941 | |
dc.description.abstract | Avoiding 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.mimetype | application/pdf | |
dc.subject | Graph theory | |
dc.subject | Graph minors | |
dc.title | On the fine structure of graphs avoiding certain complete bipartite minors | |
dc.type | dissertation | |
dc.contributor.committeeMember | Akram Aldroubi | |
dc.contributor.committeeMember | Paul Edelman | |
dc.contributor.committeeMember | Michael Mihalik | |
dc.contributor.committeeMember | Jerry Spinrad | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2019-08-19 | |
local.embargo.lift | 2019-08-19 | |
dc.contributor.committeeChair | Mark Ellingham | |