Now showing items 1-6 of 6

• #### 5-Choosability of Planar-plus-two-edge Graphs ﻿

(University of Waterloo, 2018-01-02)
We prove that graphs that can be made planar by deleting two edges are 5-choosable. To arrive at this, first we prove an extension of a theorem of Thomassen. Second, we prove an extension of a theorem Postle and Thomas. ...
• #### Jaeger’s Strong 3-Flow Conjecture for Graphs in Low Genus Surfaces ﻿

(University of Waterloo, 2020-05-05)
In 1972, Tutte posed the 3-Flow Conjecture: that all 4-edge-connected graphs have a nowhere zero 3-flow. This was extended by Jaeger et al. (1992) to allow vertices to have a prescribed, possibly non-zero difference (modulo ...
• #### On Geometric Drawings of Graphs ﻿

(University of Waterloo, 2018-04-18)
This thesis is about geometric drawings of graphs and their topological generalizations. First, we study pseudolinear drawings of graphs in the plane. A pseudolinear drawing is one in which every edge can be extended ...
• #### Planar graphs without 3-cycles and with 4-cycles far apart are 3-choosable ﻿

(University of Waterloo, 2016-09-16)
A graph G is said to be L-colourable if for a given list assignment L = {L(v)|v ∈ V (G)} there is a proper colouring c of G such that c(v) ∈ L(v) for all v in V (G). If G is L-colourable for all L with |L(v)| ≥ k for all ...
• #### Simple Drawings of Kn from Rotation Systems ﻿

(University of Waterloo, 2021-10-06)
A complete rotation system on n vertices is a collection of n cyclic permutations of the elements [n]\{i}, for i∈[n]. If D is a drawing of a labelled graph, then a rotation at vertex v is the cyclic ordering of the edges ...
• #### Thomassen’s 5-Choosability Theorem Extends to Many Faces ﻿

(University of Waterloo, 2021-09-10)
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 ...

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