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Local properties of graphs with large chromatic number
dc.contributor.author | Davies, James | |
dc.date.accessioned | 2022-08-31 14:36:22 (GMT) | |
dc.date.available | 2022-08-31 14:36:22 (GMT) | |
dc.date.issued | 2022-08-31 | |
dc.date.submitted | 2022-08-24 | |
dc.identifier.uri | http://hdl.handle.net/10012/18679 | |
dc.description.abstract | This thesis deals with problems concerning the local properties of graphs with large chromatic number in hereditary classes of graphs. We construct intersection graphs of axis-aligned boxes and of lines in $\mathbb{R}^3$ that have arbitrarily large girth and chromatic number. We also prove that the maximum chromatic number of a circle graph with clique number at most $\omega$ is equal to $\Theta(\omega \log \omega)$. Lastly, extending the $\chi$-boundedness of circle graphs, we prove a conjecture of Geelen that every proper vertex-minor-closed class of graphs is $\chi$-bounded. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | graph theory | en |
dc.subject | colouring | en |
dc.title | Local properties of graphs with large chromatic number | en |
dc.type | Doctoral Thesis | en |
dc.pending | false | |
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.degree | Doctor of Philosophy | en |
uws-etd.embargo.terms | 0 | en |
uws.contributor.advisor | Geelen, Jim | |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.published.city | Waterloo | en |
uws.published.country | Canada | en |
uws.published.province | Ontario | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |