Now showing items 1-7 of 7

• 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. ...
• Analyzing Tree Attachments in 2-Crossing-Critical Graphs with a V8 Minor ﻿

(University of Waterloo, 2023-04-25)
The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of the graph in the plane. A graph G is k-crossing-critical if its crossing number is at least k and if every proper subgraph H ...
• Edge-disjoint Linkages in Infinite Graphs ﻿

(University of Waterloo, 2022-09-26)
The main subject of this thesis is the infinite graph version of the weak linkage conjecture by Thomassen [24]. We first prove results about the structure of the lifting graph; Theorems 2.2.8, 2.2.24, and 2.3.1. As an ...
• 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 ...
• 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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