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Now showing items 1-10 of 17

#### 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 ...

#### Core Structures in Random Graphs and Hypergraphs

(University of Waterloo, 2013-08-30)

The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, ...

#### Diameter and Rumour Spreading in Real-World Network Models

(University of Waterloo, 2015-04-20)

The so-called 'small-world phenomenon', observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network's size, typically growing as a ...

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

(University of Waterloo, 2014-05-22)

The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of a graph. A graph $G$ is $k$-crossing-critical if it has crossing number at least $k$, and any subgraph of $G$ has crossing ...

#### 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 ...

#### 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 ...

#### 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 ...