Browsing Combinatorics and Optimization by Supervisor "Richter, Bruce"
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5Choosability of Planarplustwoedge Graphs
(University of Waterloo, 20180102)We prove that graphs that can be made planar by deleting two edges are 5choosable. 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 2CrossingCritical Graphs with a V8 Minor
(University of Waterloo, 20230425)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 kcrossingcritical if its crossing number is at least k and if every proper subgraph H ... 
Edgedisjoint Linkages in Infinite Graphs
(University of Waterloo, 20220926)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 3Flow Conjecture for Graphs in Low Genus Surfaces
(University of Waterloo, 20200505)In 1972, Tutte posed the 3Flow Conjecture: that all 4edgeconnected graphs have a nowhere zero 3flow. This was extended by Jaeger et al. (1992) to allow vertices to have a prescribed, possibly nonzero difference (modulo ... 
On Geometric Drawings of Graphs
(University of Waterloo, 20180418)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 3cycles and with 4cycles far apart are 3choosable
(University of Waterloo, 20160916)A graph G is said to be Lcolourable 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 Lcolourable for all L with L(v) ≥ k for all ... 
Thomassen’s 5Choosability Theorem Extends to Many Faces
(University of Waterloo, 20210910)We prove in this thesis that planar graphs can be Lcolored, where L is a listassignment in which every vertex has a 5list except for a collection of arbitrarily large faces which have 3lists, as long as those faces ...