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

  • Symmetries 

    Foldes, Stephane (University of Waterloo, 2016-10-03)
    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 Polynomial-time Path-following Interior-point Methods with Local Superlinear Convergence 

    Zhang, Shuxin (University of Waterloo, 2016-09-30)
    Interior-point methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interior-point methods over other approaches are: (1) robust global convergence, and (2) the ...
  • FACES OF MATCHING POLYHEDRA 

    Pulleyblank, William R. (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 ...
  • Packing and Covering Odd (u,v)-trails in a Graph 

    Ibrahimpur, Sharat (University of Waterloo, 2016-09-27)
    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 

    Romero Barbosa, Julian (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 ...
  • Planar graphs without 3-cycles and with 4-cycles far apart are 3-choosable 

    Sullivan, Matthew (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 ...
  • Computing the Residue Class of Partition Numbers 

    Shuldiner, Pavel (University of Waterloo, 2016-09-14)
    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 

    Giles, Frederick Richard (University of Waterloo, 2016-09-12)
    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 

    Rahimi, Fahimeh (University of Waterloo, 2016-09-02)
    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 

    Sun, Hao (University of Waterloo, 2016-08-30)
    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 k-th set. This is a variant of the well-known vertex separator ...
  • Cyclically 5-Connected Graphs 

    Chen, Da Qi (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. ...
  • Unavoidable Minors of Large 5-Connected Graphs 

    Shantanam, Abhinav (University of Waterloo, 2016-08-24)
    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 

    Graf, Alessandra (University of Waterloo, 2016-08-24)
    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 

    Yee, Randy (University of Waterloo, 2016-08-23)
    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 

    Lagzi, Saman (University of Waterloo, 2016-08-17)
    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 

    Chan, Aaron C.S. (University of Waterloo, 2016-06-10)
    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 

    Szestopalow, Michael (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 ...
  • Inner approximation of convex cones via primal-dual ellipsoidal norms 

    Xie, Miaolan (University of Waterloo, 2016-05-13)
    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 ...
  • Subdividing the cd-index 

    Dornian, Patrick (University of Waterloo, 2016-04-28)
    This thesis aims to give the reader an introduction and overview of the cd-index of a poset, as well as establish some new results. We give a combinatorial proof of Ehrenborg and Karu's cd-index subdivision decomposition ...
  • Recognizing Even-Cycle and Even-Cut Matroids 

    Heo, Cheolwon (University of Waterloo, 2016-04-27)
    Even-cycle and even-cut matroids are classes of binary matroids that generalize respectively graphic and cographic matroids. We give algorithms to check membership for these classes of matroids. We assume that the matroids ...

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