Browsing Mathematics (Faculty of) by Subject "graph coloring"
Now showing items 17 of 7

Algebraic Analysis of VertexDistinguishing EdgeColorings
(University of Waterloo, 2006)Vertexdistinguishing edgecolorings (vdec colorings) are a restriction of proper edgecolorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ... 
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2019)It is an open problem whether the 3coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3colorable ... 
Cliques, Degrees, and Coloring: Expanding the ω, Δ, χ paradigm
(University of Waterloo, 20190809)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, 20210823)The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly highdimensional finite set. It is often the case that the set is so large that ... 
List 3Coloring Graphs with No Induced P6+rP3
(Springer Nature, 20210101)For an integer t, we let Pt denote the tvertex path. We write H+G for the disjoint union of two graphs H and G, and for an integer r and a graph H, we write rH for the disjoint union of r copies of H. We say that a graph ... 
Partitioning Pauli Operators: in Theory and in Practice
(University of Waterloo, 20190904)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 5Choosability Theorem Extends to Many Faces
(University of Waterloo, 20210910)We prove in this thesis that planar graphs can be Lcolored, where L is a listassignment in which every vertex has a 5list except for a collection of arbitrarily large faces which have 3lists, as long as those faces ...