Browsing Theses by Subject "graph coloring"
Now showing items 1-5 of 5
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Algebraic Analysis of Vertex-Distinguishing Edge-Colorings
(University of Waterloo, 2006)Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ... -
Cliques, Degrees, and Coloring: Expanding the ω, Δ, χ paradigm
(University of Waterloo, 2019-08-09)Many of the most celebrated and influential results in graph coloring, such as Brooks' Theorem and Vizing's Theorem, relate a graph's chromatic number to its clique number or maximum degree. Currently, several of the most ... -
Convex Algebraic Geometry Approaches to Graph Coloring and Stable Set Problems
(University of Waterloo, 2021-08-23)The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly high-dimensional finite set. It is often the case that the set is so large that ... -
Partitioning Pauli Operators: in Theory and in Practice
(University of Waterloo, 2019-09-04)Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in the variational quantum eigensolver. Simultaneously measuring sets of operators allows for fewer measurements and an ... -
Thomassen’s 5-Choosability Theorem Extends to Many Faces
(University of Waterloo, 2021-09-10)We prove in this thesis that planar graphs can be L-colored, where L is a list-assignment in which every vertex has a 5-list except for a collection of arbitrarily large faces which have 3-lists, as long as those faces ...