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Now showing items 11-18 of 18

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Constructing Cospectral and Comatching Graphs

(University of Waterloo, 2019-07-18)

The matching polynomial is a graph polynomial that does not only have interesting mathematical properties, but also possesses meaningful applications in physics and chemistry. For a simple graph, the matching polynomial ...

#### 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: ...

#### 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 ...