Browsing Theses by Subject "Graph Theory"
Now showing items 1-19 of 19
-
Applied Hilbert's Nullstellensatz for Combinatorial Problems
(University of Waterloo, 2016-09-23)Various feasibility problems in Combinatorial Optimization can be stated using systems of polynomial equations. Determining the existence of a \textit{stable set} of a given size, finding the \textit{chromatic number} of ... -
Automated Selection of Modelling Coordinates for Forward Dynamic Analysis of Multibody Systems
(University of Waterloo, 2006)Modelling mechanical systems using symbolic equations can provide many advantages over the more widely-used numerical methods of modelling these systems. The use of symbolic equations produces more efficient models, which ... -
Circle Graph Obstructions
(University of Waterloo, 2017-08-31)In this thesis we present a self-contained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excluded-minor characterization ... -
The Complexity of Network Design for s-t Eff ective Resistance
(University of Waterloo, 2018-08-23)We consider a new problem of designing a network with small $s$-$t$ effective resistance. In this problem, we are given an undirected graph $G=(V,E)$ where each edge $e$ has a cost $c_e$ and a resistance $r_e$, two ... -
Cyclically 5-Connected Graphs
(University of Waterloo, 2016-08-29)Tutte's Four-Flow Conjecture states that every bridgeless, Petersen-free graph admits a nowhere-zero 4-flow. This hard conjecture has been open for over half a century with no significant progress in the first forty years. ... -
Equiangular Lines and Antipodal Covers
(University of Waterloo, 2010-09-22)It is not hard to see that the number of equiangular lines in a complex space of dimension $d$ is at most $d^{2}$. A set of $d^{2}$ equiangular lines in a $d$-dimensional complex space is of significant importance in Quantum ... -
Highly Non-Convex Crossing Sequences
(University of Waterloo, 2012-05-18)For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence ... -
List Coloring Some Classes of 1-Planar Graphs
(University of Waterloo, 2021-12-23)In list coloring we are given a graph G and a list assignment for G which assigns to each vertex of G a list of possible colors. We wish to find a coloring of the vertices of G such that each vertex uses a color from its ... -
Matchings and Covers in Hypergraphs
(University of Waterloo, 2016-05-17)In this thesis, we study three variations of matching and covering problems in hypergraphs. The first is motivated by an old conjecture of Ryser which says that if $\mcH$ is an $r$-uniform, $r$-partite hypergraph which ... -
Minimum Crossing Problems on Graphs
(University of Waterloo, 2007-01-19)This thesis will address several problems in discrete optimization. These problems are considered hard to solve. However, good approximation algorithms for these problems may be helpful in approximating problems in ... -
Minimum Number of Triangles of K5 Descendants
(University of Waterloo, 2022-01-26)In the study of Quantum Field Theory and Feynman Periods, the operation of double triangle expansion plays an important role. This is largely due to double triangle expansions not affecting the maximum weight of the ... -
Planar graphs without 3-cycles and with 4-cycles far apart are 3-choosable
(University of Waterloo, 2016-09-16)A graph G is said to be L-colourable if for a given list assignment L = {L(v)|v ∈ V (G)} there is a proper colouring c of G such that c(v) ∈ L(v) for all v in V (G). If G is L-colourable for all L with |L(v)| ≥ k for all ... -
Properties of graphs with large girth
(University of Waterloo, 2008-01-24)This thesis is devoted to the analysis of a class of iterative probabilistic algorithms in regular graphs, called locally greedy algorithms, which will provide bounds for graph functions in regular graphs with ... -
Properties of Stable Matchings
(University of Waterloo, 2010-12-17)Stable matchings were introduced in 1962 by David Gale and Lloyd Shapley to study the college admissions problem. The seminal work of Gale and Shapley has motivated hundreds of research papers and found applications in ... -
Results on Chromatic Polynomials Inspired by a Correlation Inequality of G.E. Farr
(University of Waterloo, 2018-09-25)In1993 Graham Farr gave a proof of a correlation inequality involving colourings of graphs. His work eventually led to a conjecture that number of colourings of a graph with certain properties gave a log-concave sequence. ... -
Simultaneous Graph Representation Problems
(University of Waterloo, 2011-02-18)Many graphs arising in practice can be represented in a concise and intuitive way that conveys their structure. For example: A planar graph can be represented in the plane with points for vertices and non-crossing curves ... -
Simultaneously Embedding Planar Graphs at Fixed Vertex Locations
(University of Waterloo, 2010-05-18)We discuss the problem of embedding planar graphs onto the plane with pre-specified vertex locations. In particular, we introduce a method for constructing such an embedding for both the case where the mapping from the ... -
Symbolic Modelling and Simulation of Wheeled Vehicle Systems on Three-Dimensional Roads
(University of Waterloo, 2009-10-26)In recent years, there has been a push by automotive manufacturers to improve the efficiency of the vehicle development process. This can be accomplished by creating a computationally efficient vehicle model that has the ... -
Uniform Mixing of Quantum Walks and Association Schemes
(University of Waterloo, 2013-09-26)In recent years quantum algorithms have become a popular area of mathematical research. Farhi and Gutmann introduced the concept of a quantum walk in 1998. In this thesis we investigate mixing properties of continuous-time ...