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Now showing items 11-17 of 17

#### 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 ...

#### 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: ...

#### 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 ...

#### 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 ...