Combinatorics and Optimization
This is the collection for the University of Waterloo's Department of Combinatorics and Optimization .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits

Spectral properties of tensor products of channels
(Elsevier, 20180915)We investigate spectral properties of the tensor products of two completely positive and trace preserving linear maps (also known as quantum channels) acting on matrix algebras. This leads to an important question of when ... 
Action of degenerate Bethe operators on representations of the symmetric group
(University of Waterloo, 20180524)Degenerate Bethe operators are elements defined by explicit sums in the center of the group algebra of the symmetric group. They are useful on account of their relation to the GelfandZetlin algebra and the YoungJucysMurphy ... 
The Capacitated Matroid Median Problem
(University of Waterloo, 20180518)In this thesis, we study the capacitated generalization of the Matroid Median Problem which is a generalization of the classical clustering problem called the kMedian problem. In the capacitated matroid median problem, ... 
Extensions of Galvin's Theorem
(University of Waterloo, 20180430)We discuss problems in list coloring with an emphasis on techniques that utilize oriented graphs. Our central theme is Galvin's resolution of the Dinitz problem (Galvin. J. Comb. Theory, Ser. B 63(1), 1995, 153158). We ... 
Thin Trees in Some Families of Graphs
(University of Waterloo, 20180425)Let 𝐺=(𝑉,𝐸) be a graph and let 𝑇 be a spanning tree of 𝐺. The thinness parameter of 𝑇 denoted by 𝜌(𝑇) is the maximum over all cuts of the proportion of the edges of 𝑇 in the cut. Thin trees play an important role ... 
Ideal Clutters
(University of Waterloo, 20180424)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 ... 
On Geometric Drawings of Graphs
(University of Waterloo, 20180418)This thesis is about geometric drawings of graphs and their topological generalizations. First, we study pseudolinear drawings of graphs in the plane. A pseudolinear drawing is one in which every edge can be extended ... 
A Primal Dual Algorithm On 2Steiner Graphs
(University of Waterloo, 20180123)The Steiner Tree Problem is a fundamental network design problem, where the goal is to connect a subset of terminals of a given network at minimum cost. A major open question regarding this problem, is proving that the ... 
5Choosability of Planarplustwoedge Graphs
(University of Waterloo, 20180102)We prove that graphs that can be made planar by deleting two edges are 5choosable. To arrive at this, first we prove an extension of a theorem of Thomassen. Second, we prove an extension of a theorem Postle and Thomas. ... 
Extending Pappus' Theorem
(University of Waterloo, 20171222)Let $M_1$ and $M_2$ be matroids such that $M_2$ arises from $M_1$ by relaxing a circuithyperplane. We will prove that if $M_1$ and $M_2$ are both representable over some finite field $GF(q)$, then $M_1$ and $M_2$ have ... 
Linearlydense classes of matroids with bounded branchwidth
(University of Waterloo, 20170927)Let $M$ be a nonempty minorclosed class of matroids with bounded branchwidth that does not contain arbitrarily large simple rank$2$ matroids. For each nonnegative integer $n$ we denote by $ex(n)$ the size of the ... 
Combinatorial Arithmetic on Elliptic Curves
(University of Waterloo, 20170927)We propose a scalar multiplication technique on an elliptic curve, which operates on triples of collinear points. The computation of this operation requires a new approach to operation chains, with similarities to Montgomery ... 
On The Circuit Diameters of Some Combinatorial Polytopes
(University of Waterloo, 20170920)The combinatorial diameter of a polytope P is the maximum value of a shortest path between two vertices of P, where the path uses the edges of P only. In contrast to the combinatorial diameter, the circuit diameter of P ... 
A postquantum digital signature scheme based on supersingular isogenies
(University of Waterloo, 20170920)We present the first generalpurpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is ... 
Circle Graph Obstructions
(University of Waterloo, 20170831)In this thesis we present a selfcontained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excludedminor characterization ... 
A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 20170829)Nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique because it is easily interpretable and can discern useful features. For a given matrix M (dimension n x m) whose entries are nonnegative ... 
Stabilizing Weighted Graphs
(University of Waterloo, 20170829)An edgeweighted graph G = (V,E) is called stable if the value of a maximumweight matching equals the value of a maximumweight fractional matching. Stable graphs play an important role in some interesting game theory ... 
Some Upper and Lower Bounds regarding Query Complexity
(University of Waterloo, 20170829)Query complexity is one of the several notions of complexity de ned to measure the cost of algorithms. It plays an important role in demonstrating the quantum advantage, that quantum computing is faster than classical ... 
Technology Diffusion on Spiders
(University of Waterloo, 20170829)There has been significant research about cascade effects that occur when information is spread through a network. Most models of such cascade effects are highlylocalised, which means that they assume a node’s behaviour ... 
Generating Functions for Hyperbolic Plane Tessellations
(University of Waterloo, 20170828)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 ...