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Now showing items 11-17 of 17

#### Multigraphs with High Chromatic Index

(University of Waterloo, 2009-07-22)

In this thesis we take a specialized approach to edge-colouring by focusing exclusively on multigraphs with high chromatic index. The bulk of our results can be classified into three categories. First, we prove results ...

#### Properties of random graphs

(University of Waterloo, 2008-09-23)

The thesis describes new results for several problems in random graph theory.
The first problem relates to the uniform random graph model in
the supercritical phase; i.e. a graph, uniformly distributed, on $n$ vertices
and ...

#### Algebraic Methods for Reducibility in Nowhere-Zero Flows

(University of Waterloo, 2007-09-25)

We study reducibility for nowhere-zero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counter-example to some conjecture. We derive algebraic proofs of ...

#### Acyclic Colouring of Graphs on Surfaces

(University of Waterloo, 2018-09-04)

An acyclic k-colouring of a graph G is a proper k-colouring of G with no bichromatic cycles. In 1979, Borodin proved that planar graphs are acyclically 5-colourable, an analog of the Four Colour Theorem. Kawarabayashi and ...

#### Establishing a Connection Between Graph Structure, Logic, and Language Theory

(University of Waterloo, 2015-09-08)

The field of graph structure theory was given life by the Graph Minors Project of Robertson and Seymour, which developed many tools for understanding the way graphs relate to each other and culminated in the proof of the ...

#### 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 ...

#### Density and Structure of Homomorphism-Critical Graphs

(University of Waterloo, 2018-08-22)

Let $H$ be a graph. A graph $G$ is $H$-critical if every proper subgraph of $G$ admits a homomorphism to $H$, but $G$ itself does not. In 1981, Jaeger made the following conjecture concerning odd-cycle critical graphs: ...