Browsing Combinatorics and Optimization by Title
Now showing items 424-434 of 434
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Unavoidable Minors of Large 5-Connected Graphs
(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 ... -
Uniform Generation of Graphical Realizations of Joint Degree Matrices
(University of Waterloo, 2023-09-21)In this thesis, we introduce JDM_GEN, an algorithm designed to uniformly generate graphical realizations of a given joint degree matrix. Amanatidis and Kleer previously employed an MCMC-based method to address this ... -
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 ... -
Uniform Mixing on Cayley Graphs over Z_3^d
(University of Waterloo, 2014-05-22)This thesis investigates uniform mixing on Cayley graphs over Z_3^d. We apply Mullin's results on Hamming quotients, and characterize the 2(d+2)-regular connected Cayley graphs over Z_3^d that admit uniform mixing at time ... -
Uniqueness and Complexity in Generalised Colouring
(University of Waterloo, 2003)The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition ... -
Variational Spectral Analysis
(University of Waterloo, 2000)We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the eigenvalues of a real symmetric matrix argument, as well as {it absolutely symmetric} functions of the singular values ... -
Variations on a Theme: Graph Homomorphisms
(University of Waterloo, 2013-08-30)This thesis investigates three areas of the theory of graph homomorphisms: cores of graphs, the homomorphism order, and quantum homomorphisms. A core of a graph X is a vertex minimal subgraph to which X admits a ... -
Vertex Stabilizers for Network Bargaining Games
(University of Waterloo, 2022-03-04)Network bargaining games form a prominent class of examples of game theory problems defined on graphs, where vertices represent players, and edges represent their possible interactions. An instance of a \emph{network ... -
A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function
(The Electronic Journal of Combinatorics, 2021-04-09)This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version ofXB, show that this function admits a ... -
Welch Bounds and Quantum State Tomography
(University of Waterloo, 2008-12-22)In this thesis we investigate complete systems of MUBs and SIC-POVMs. These are highly symmetric sets of vectors in Hilbert space, interesting because of their applications in quantum tomography, quantum cryptography and ... -
Worst-Case to Average-Case Reductions for the SIS Problem: Tightness and Security
(University of Waterloo, 2019-07-30)We present a framework for evaluating the concrete security assurances of cryptographic constructions given by the worst-case SIVP_γ to average-case SIS_{n,m,q,β} reductions. As part of this analysis, we present the tightness ...