Thomassen’s 5-Choosability Theorem Extends to Many Faces
| dc.contributor.author | Nevin, Joshua | |
| dc.date.accessioned | 2021-09-10T18:31:59Z | |
| dc.date.available | 2021-09-10T18:31:59Z | |
| dc.date.issued | 2021-09-10 | |
| dc.date.submitted | 2021-08-17 | |
| dc.description.abstract | We prove in this thesis that planar graphs can be L-colored, where L is a list-assignment in which every vertex has a 5-list except for a collection of arbitrarily large faces which have 3-lists, as long as those faces are at least a constant distance apart. Such a result is analogous to Thomassen’s 5-choosability proof where arbitrarily many faces, rather than just one face, are permitted to have 3-lists. This result can also be thought of as a stronger form of a conjecture of Albertson which was solved in 2012 and asked whether a planar graph can be 5-list-colored even if it contains distant precolored vertices. Our result has useful applications in proving that drawings with arbitrarily large pairwise far-apart crossing structures are 5-choosable under certain conditions, and we prove one such result at the end of this thesis. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/17374 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | graph coloring | en |
| dc.subject | topological graph theory | en |
| dc.subject | list coloring | en |
| dc.title | Thomassen’s 5-Choosability Theorem Extends to Many Faces | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Combinatorics and Optimization | en |
| uws-etd.degree.discipline | Combinatorics and Optimization | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Richter, Bruce | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |