Now showing items 175-194 of 433

    • A Generalization to Signed Graphs of a Theorem of Sergey Norin and Robin Thomas 

      Horrocks, Courtney (University of Waterloo, 2019-12-19)
      In this thesis we characterize the minimal non-planar extensions of a signed graph. We consider the following question: Given a subdivision of a planar signed graph (G, Σ), what are the minimal structures that can be added ...
    • Generating Functions for Hyperbolic Plane Tessellations 

      Xie, Jiale (University of Waterloo, 2017-08-28)
      For a hyperbolic plane tessellation there is a generating function with respect to the distance. This generating function is the same as the growth function of a group of isometries of hyperbolic plane that acts regularly ...
    • Generation and properties of random graphs and analysis of randomized algorithms 

      Gao, Pu (University of Waterloo, 2010-01-22)
      We study a new method of generating random $d$-regular graphs by repeatedly applying an operation called pegging. The pegging algorithm, which applies the pegging operation in each step, is a method of generating large ...
    • Genus one partitions 

      Yip, Martha (University of Waterloo, 2006)
      We obtain a tight upper bound for the genus of a partition, and calculate the number of partitions of maximal genus. The generating series for genus zero and genus one rooted hypermonopoles is obtained in closed form ...
    • Geometric Ramifications of the Lovász Theta Function and Their Interplay with Duality 

      de Carli Silva, Marcel Kenji (University of Waterloo, 2013-08-30)
      The Lovasz theta function and the associated convex sets known as theta bodies are fundamental objects in combinatorial and semidefinite optimization. They are accompanied by a rich duality theory and deep connections ...
    • Geometry of convex sets arising from hyperbolic polynomials 

      Myklebust, Tor Gunnar Josefsson Jay (University of Waterloo, 2008-09-09)
      This thesis focuses on convex sets and convex cones defined using hyperbolic polynomials. We first review some of the theory of convex sets in $\R^d$ in general. We then review some classical algebraic theorems concerning ...
    • Goldberg's conjecture is true for random multigraphs 

      Haxell, Penny; Krivelevich, Michael; Kronenberg, Gal (Elsevier, 2019-09)
      In the 70s, Goldberg, and independently Seymour, conjectured that for any multigraph G, the chromatic index χ′(G) satisfies χ′(G) ≤ max{∆(G)+1,⌈ρ(G)⌉}, where ρ(G) = max\{\frac {e(G[S])}{\lfloor|S|/2\rfloor} \mid S\subseteq ...
    • Graph Coverings with Few Eigenvalues or No Short Cycles 

      Levit, Maxwell (University of Waterloo, 2023-05-18)
      This thesis addresses the extent of the covering graph construction. How much must a cover X resemble the graph Y that it covers? How much can X deviate from Y? The main statistics of X and Y which we will measure are their ...
    • Graph-Theoretic Techniques for Optimizing NISQ Algorithms 

      Jena, Andrew (University of Waterloo, 2024-02-15)
      Entering the NISQ era, the search for useful yet simple quantum algorithms is perhaps of more importance now than it may ever be in the future. In place of quantum walks, the quantum Fourier transform, and asymptotic results ...
    • Graphical CSS Code Transformation Using ZX Calculus 

      Li, Sarah Meng (University of Waterloo, 2023-12-21)
      In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps ...
    • The Graphs of HU+00E4ggkvist & Hell 

      Roberson, David E. (University of Waterloo, 2009-01-19)
      This thesis investigates HU+00E4ggkvist & Hell graphs. These graphs are an extension of the idea of Kneser graphs, and as such share many attributes with them. A variety of original results on many different properties of ...
    • H-colouring Pt-free graphs in subexponential time 

      Groenland, Carla; Okrasa, Karolina; Rzążewski, Paweł; Scott, Alex; Seymour, Paul; Spirkl, Sophie (Elsevier, 2019-08-31)
      A graph is called Pt-free if it does not contain the path on t vertices as an induced subgraph. Let H be a multigraph with the property that any two distinct vertices share at most one common neighbour. We show that the ...
    • Hamilton Paths in Generalized Petersen Graphs 

      Pensaert, William (University of Waterloo, 2002)
      This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is ...
    • Hardness results and approximation algorithms for some problems on graphs 

      Aazami, Ashkan (University of Waterloo, 2008-12-17)
      This thesis has two parts. In the first part, we study some graph covering problems with a non-local covering rule that allows a "remote" node to be covered by repeatedly applying the covering rule. In the second part, we ...
    • Highly Non-Convex Crossing Sequences 

      McConvey, Andrew (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 ...
    • Homomorphic Encryption 

      Weir, Brandon (University of Waterloo, 2013-01-24)
      In this thesis, we provide a summary of fully homomorphic encryption, and in particular, look at the BGV encryption scheme by Brakerski, Gentry, and Vaikuntanathan; as well the DGHV encryption scheme by van Dijk, Gentry, ...
    • Hurwitz Trees and Tropical Geometry 

      Akeyr, Garnet Jonathan (University of Waterloo, 2016-01-21)
      The lifting problem in algebraic geometry asks when a finite group G acting on a curve defined over characteristic p > 0 lifts to characteristic 0. One object used in the study of this problem is the Hurwitz tree, which ...
    • Hyperpfaffians in Algebraic Combinatorics 

      Redelmeier, Daniel (University of Waterloo, 2006)
      The pfaffian is a classical tool which can be regarded as a generalization of the determinant. The hyperpfaffian, which was introduced by Barvinok, generalizes the pfaffian to higher dimension. This was further ...
    • Ideal Clutters 

      Abdi, Ahmad (University of Waterloo, 2018-04-24)
      Let E be a finite set of elements, and let C be a family of subsets of E called members. We say that C is a clutter over ground set E if no member is contained in another. The clutter C is ideal if every extreme point of ...
    • Implementing the Castryck-Decru attack on SIDH with general primes 

      Laflamme, Jeanne (University of Waterloo, 2024-01-09)
      With the rapid progress of quantum computers in recent years, efforts have been made to standardize new public-key cryptographic protocols which would be secure against them. One of the schemes in contention was Supersingular ...

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