dc.contributor.author | Saleh, Rana | |
dc.date.accessioned | 2021-09-28 14:22:49 (GMT) | |
dc.date.available | 2021-09-28 14:22:49 (GMT) | |
dc.date.issued | 2021-09-28 | |
dc.date.submitted | 2021-08-30 | |
dc.identifier.uri | http://hdl.handle.net/10012/17563 | |
dc.description.abstract | In this thesis, we study correspondence colouring and its applications to list colouring
and delay colouring. We give a detailed exposition of the paper of Dvořák, and Postle
introducing correspondence colouring.
Moreover, we generalize two important results in delay colouring. The first is a result
by Georgakopoulos, stating that cubic graphs are 4-delay colourable. We show that delay
colouring can be formulated as an instance of correspondence colouring. Then we show that
the modified line graph of a cubic bipartite graph is generally 4-correspondence colourable,
using a Brooks’ type theorem for correspondence colouring. This allows us to give a more
simple proof of a stronger result. The second result is one by Edwards and Kennedy, which
states that quartic bipartite graphs are 5-delay colourable. We introduce the notion of p-cyclic correspondence colouring which is a type of correspondence colouring that generalizes
delay colouring. We then prove that the modified line graph of a quartic bipartite graph
is 5-cyclic correspondence colourable using the Combinatorial Nullstellensatz.
We also show that the maximum DP-chromatic number of any cycle plus triangles (CPT)
graph is 4. We construct a CPT graph with DP-chromatic number at least 4. Moreover, the
upper bound follows easily from the Brooks’ type theorem for correspondence colouring.
Finally, we do a preliminary investigation into using parity techniques in correspondence
colouring to prove that CPT graphs are 3-choosable. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | Combinatorial Nullstellensatz | en |
dc.subject | Correspondence Colouring | en |
dc.subject | DP colouring | en |
dc.subject | list colouring | en |
dc.subject | delay colouring | en |
dc.subject | cycle plus triangles graphs | en |
dc.title | Correspondence Colouring and its Applications to List Colouring and Delay Colouring | en |
dc.type | Master 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 | Master of Mathematics | en |
uws-etd.embargo.terms | 0 | en |
uws.contributor.advisor | Haxell, Penny | |
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 |