Local properties of graphs with large chromatic number
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.
Collections
Cite this version of the work
James Davies
(2022).
Local properties of graphs with large chromatic number. UWSpace.
http://hdl.handle.net/10012/18679
Other formats