Combinatorics and Optimization Theses & Dissertations
This is the collection for the University of Waterloo's Department of Combinatorics and Optimization theses & dissertations.
Graduate students can submit a copy of their electronic thesis or dissertation to this collection to meet their degree requirements.
Recent Submissions

On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 20161221)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$minor have? This is a natural analogue of questions asked about the density of graphs in minorclosed ... 
Structure in Stable Matching Problems
(University of Waterloo, 20161214)In this thesis we provide two contributions to the study of structure in stable matching problems. The first contribution is a short new proof for the integrality of Rothblum’s linear description of the convex hull of ... 
Symmetries
(University of Waterloo, 20161003)Automorphisms of graphs, hypergraphs and disgraphs are investigated. The invariance of the chromatic polynomial in the rotor effect is disproved. New invariance results are obtained. It is shown that given any integer k ... 
On Polynomialtime Pathfollowing Interiorpoint Methods with Local Superlinear Convergence
(University of Waterloo, 20160930)Interiorpoint methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interiorpoint methods over other approaches are: (1) robust global convergence, and (2) the ... 
FACES OF MATCHING POLYHEDRA
(University of Waterloo, 20160930)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 ... 
Packing and Covering Odd (u,v)trails in a Graph
(University of Waterloo, 20160927)In this thesis, we investigate the problem of packing and covering odd $(u,v)$trails in a graph. A $(u,v)$trail is a $(u,v)$walk that is allowed to have repeated vertices but no repeated edges. We call a trail \emph{odd} ... 
Applied Hilbert's Nullstellensatz for Combinatorial Problems
(University of Waterloo, 20160923)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 ... 
Planar graphs without 3cycles and with 4cycles far apart are 3choosable
(University of Waterloo, 20160916)A graph G is said to be Lcolourable 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 Lcolourable for all L with L(v) ≥ k for all ... 
Computing the Residue Class of Partition Numbers
(University of Waterloo, 20160914)In 1919, Ramanujan initiated the study of congruence properties of the integer partition function $p(n)$ by showing that $$p(5n+4) \equiv 0 \mod{5}$$ and $$p(7n+5) \equiv 0 \mod{7}$$ hold for all integers $n$. These results ... 
SUBMODULAR FUNCTIONS, GRAPHS AND INTEGER POLYHEDRA
(University of Waterloo, 20160912)This thesis is a study of the faces of certain combinatorially defined polyhedra. In particular, we examine the vertices and facets of these polyhedra. Chapter 2 contains the essential mathematical background in polyhedral ... 
Covering Graphs and Equiangular Tight Frames
(University of Waterloo, 20160902)Recently, there has been huge attention paid to equiangular tight frames and their constructions, due to the fact that the relationship between these frames and quantum information theory was established. One of the problems ... 
ADMM for SDP Relaxation of GP
(University of Waterloo, 20160830)We consider the problem of partitioning the set of nodes of a graph G into k sets of given sizes in order to minimize the cut obtained after removing the kth set. This is a variant of the wellknown vertex separator ... 
Cyclically 5Connected Graphs
(University of Waterloo, 20160829)Tutte's FourFlow Conjecture states that every bridgeless, Petersenfree graph admits a nowherezero 4flow. This hard conjecture has been open for over half a century with no significant progress in the first forty years. ... 
Unavoidable Minors of Large 5Connected Graphs
(University of Waterloo, 20160824)This thesis shows that, for every positive integer $n \geq 5$, there exists a positive integer $N$ such that every $5$connected graph with at least $N$ vertices has a minor isomorphic to one of thirty explicitly defined ... 
On the Strongly Connected Components of Random Directed Graphs with Given Degree Sequences
(University of Waterloo, 20160824)A strongly connected component of a directed graph G is a maximal subgraph H of G such that for each pair of vertices u and v in H, there is a directed path from u to v and a directed path from v to u in H. A strongly ... 
On the effectiveness of isogeny walks for extending cover attacks on elliptic curves
(University of Waterloo, 20160823)Cryptographic systems based on the elliptic curve discrete logarithm problem (ECDLP) are widely deployed in the world today. In order for such a system to guarantee a particular security level, the elliptic curve selected ... 
A Study of Time Representation in a Class of Short Term Scheduling Problems
(University of Waterloo, 20160817)The problem of scheduling operations has received significant attention from academia and industrial practitioners in the past few decades. A key decision in various scheduling operations problems is when to perform an ... 
Combinatorial Methods for Enumerating Maps in Surfaces of Arbitrary Genus
(University of Waterloo, 20160610)The problem of map enumeration is one that has been studied intensely for the past half century. Early work on this subject included the works of Tutte for various types of rooted planar maps and the works of Brown for ... 
Matchings and Covers in Hypergraphs
(University of Waterloo, 20160517)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 ... 
Inner approximation of convex cones via primaldual ellipsoidal norms
(University of Waterloo, 20160513)We study ellipsoids from the point of view of approximating convex sets. Our focus is on finding largest volume ellipsoids with specified centers which are contained in certain convex cones. After reviewing the related ...