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Now showing items 1-10 of 16

#### 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 ...

#### 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 ...

#### 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 ...

#### Self-Dual Graphs

(University of Waterloo, 2002)

The study of self-duality has attracted some attention over the past decade. A good deal of research in that time has been done on constructing and classifying all self-dual graphs and in particular polyhedra. We ...

#### Morphing planar triangulations

(University of Waterloo, 2014-06-09)

A morph between two drawings of the same graph can be thought of as a continuous deformation between the two given drawings. A morph is linear if every vertex moves along a straight line segment from its initial position ...

#### 2-crossing critical graphs with a V8 minor

(University of Waterloo, 2012-01-17)

The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a ...

#### FACES OF MATCHING POLYHEDRA

(University of Waterloo, 2016-09-30)

Let G = (V, E, ~) be a finite loopless graph, let
b=(bi:ieV) be a vector of positive integers. A
feasible matching is a vector X = (x.: j e: E)
J
of nonnegative
integers such that for each node i of G, the sum of ...

#### Variations on a Theme: Graph Homomorphisms

(University of Waterloo, 2013-08-30)

This thesis investigates three areas of the theory of graph homomorphisms: cores of graphs, the homomorphism order, and quantum homomorphisms.
A core of a graph X is a vertex minimal subgraph to which X admits a ...

#### Hamilton Paths in Generalized Petersen Graphs

(University of Waterloo, 2002)

This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is ...