Show simple item record

dc.contributor.authorSaleh, Rana
dc.date.accessioned2021-09-28 14:22:49 (GMT)
dc.date.available2021-09-28 14:22:49 (GMT)
dc.date.issued2021-09-28
dc.date.submitted2021-08-30
dc.identifier.urihttp://hdl.handle.net/10012/17563
dc.description.abstractIn 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.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectCombinatorial Nullstellensatzen
dc.subjectCorrespondence Colouringen
dc.subjectDP colouringen
dc.subjectlist colouringen
dc.subjectdelay colouringen
dc.subjectcycle plus triangles graphsen
dc.titleCorrespondence Colouring and its Applications to List Colouring and Delay Colouringen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws-etd.embargo.terms0en
uws.contributor.advisorHaxell, Penny
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record


UWSpace

University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages