Now showing items 134-153 of 433

    • Edge coloring multigraphs without small dense subsets 

      Haxell, P.E.; Kierstead, H.A. (Elsevier, 2015-12-06)
      One consequence of a long-standing conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose $G$ is a multigraph with maximum degree $\Delta$, such that no vertex ...
    • Edge State Transfer 

      Chen, Qiuting (University of Waterloo, 2019-01-11)
      Let G be a graph and let t be a positive real number. Then the evolution of the continuous quantum walk defined on G is described by the transition matrix U(t)=exp(itH).The matrix H is called Hamiltonian. So far the most ...
    • Edge-disjoint Linkages in Infinite Graphs 

      Assem Abd-AlQader Mahmoud, Amena (University of Waterloo, 2022-09-26)
      The main subject of this thesis is the infinite graph version of the weak linkage conjecture by Thomassen [24]. We first prove results about the structure of the lifting graph; Theorems 2.2.8, 2.2.24, and 2.3.1. As an ...
    • The Edmonds-Giles Conjecture and its Relaxations 

      Hwang, Steven (University of Waterloo, 2022-12-23)
      Given a directed graph, a directed cut is a cut with all arcs oriented in the same direction, and a directed join is a set of arcs which intersects every directed cut at least once. Edmonds and Giles conjectured for all ...
    • Efficient Composition of Discrete Time Quantum Walks 

      Lou, Xingliang (University of Waterloo, 2017-01-20)
      It is well known that certain search problems are efficiently solved by quantum walk algorithms. Of particular interest are those problems whose efficient solutions involve nesting of search algorithms. The nesting of ...
    • Efficient Integer Representations for Cryptographic Operations 

      Muir, James (University of Waterloo, 2004)
      Every positive integer has a unique radix 2 representation which uses the digits {0,1}. However, if we allow digits other than 0 and 1, say {0,1,-1}, then a positive integer has many representations. Of these ...
    • Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation 

      Xiong, Xin (University of Waterloo, 2014-01-23)
      This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of two directed edge separator methods, the ...
    • Efficient Pairings on Various Platforms 

      Grewal, Gurleen (University of Waterloo, 2012-05-14)
      Pairings have found a range of applications in many areas of cryptography. As such, to utilize the enormous potential of pairing-based protocols one needs to efficiently compute pairings across various computing platforms. ...
    • Efficient Trust Region Subproblem Algorithms 

      Ye, Heng (University of Waterloo, 2011-09-29)
      The Trust Region Subproblem (TRS) is the problem of minimizing a quadratic (possibly non-convex) function over a sphere. It is the main step of the trust region method for unconstrained optimization problems. Two cases may ...
    • Ehrhart Theory and Unimodular Decompositions of Lattice Polytopes 

      Tam, Ricci Yik Chi (University of Waterloo, 2015-01-20)
      Ehrhart theory studies the behaviour of lattice points contained in dilates of lattice polytopes. We provide an introduction to Ehrhart theory. In particular, we prove Ehrhart's Theorem, Stanley Non-negativity, and ...
    • Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems 

      Wang, Ningchuan (University of Waterloo, 2014-09-03)
      The Graph Partitioning problems are hard combinatorial optimization problems. We are interested in both lower bounds and upper bounds. We introduce several methods including basic eigenvalue and projected eigenvalue ...
    • Entropic Matroids and Their Representation 

      Abbe, Emmanuel; Spirkl, Sophie (Multidisciplinary Digital Publishing Institute, 2019)
      This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have ...
    • Entropy and Graphs 

      Changiz Rezaei, Seyed Saeed (University of Waterloo, 2014-01-23)
      The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and ...
    • Enumerating matroid extensions 

      Redlin Hume, Shayla (University of Waterloo, 2023-09-01)
      This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ...
    • Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality 

      Sloss, Craig (University of Waterloo, 2011-04-25)
      The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This ...
    • Enumerative Applications of Integrable Hierarchies 

      Carrell, Sean (University of Waterloo, 2015-05-21)
      Countably infinite families of partial differential equations such as the Kadomtzev - Petviashvili (KP) hierarchy and the B-type KP (BKP) hierarchy have received much interest in the mathematical and theoretical physics ...
    • Enumerative perspectives on chord diagrams 

      Nabergall, Lukas (University of Waterloo, 2022-10-07)
      The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ...
    • Equiangular Lines and Antipodal Covers 

      Mirjalalieh Shirazi, Mirhamed (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 ...
    • The Erdős Pentagon Problem 

      Siy, Kris (University of Waterloo, 2018-12-20)
      The Erdős pentagon problem asks about the maximum number of copies of C_5 that one can find in a triangle-free graph. This problem was posed in 1984, but was not resolved until 2012. In this thesis, we aim to capture the ...
    • Error Bounds and Singularity Degree in Semidefinite Programming 

      Sremac, Stefan (University of Waterloo, 2020-01-24)
      An important process in optimization is to determine the quality of a proposed solution. This usually entails calculation of the distance of a proposed solution to the optimal set and is referred to as forward error. ...

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