Browsing Mathematics (Faculty of) by Supervisor "Biedl, Therese"
Now showing items 19 of 9

A 2Approximation for the Height of Maximal Outerplanar Graph Drawings
(University of Waterloo, 20160818)In this thesis, we study drawings of maximal outerplanar graphs that place vertices on integer coordinates. We introduce a new class of graphs, called umbrellas, and a new method of splitting maximal outerplanar graphs ... 
AreaEfficient Drawings of Outer1Planar Graphs
(University of Waterloo, 20200929)We study areaefficient drawings of planar graphs: embeddings of graphs on an integer grid so that the bounding box of the drawing is minimized. Our focus is on the class of outer1planar graphs: the family of planar ... 
Bounds on Maximum Matchings in 1Planar Graphs
(University of Waterloo, 20190129)In this thesis, we study lower bounds on maximum matchings in 1planar graphs. We expand upon the tools used for proofs of matching bounds in other classes of graphs as well as some original ideas in order to find these ... 
Building a larger class of graphs for efficient reconfiguration of vertex colouring
(University of Waterloo, 20200513)A $k$colouring of a graph $G$ is an assignment of at most $k$ colours to the vertices of $G$ so that adjacent vertices are assigned different colours. The reconfiguration graph of the $k$colourings, $\mathcal{R}_k(G)$, ... 
Graph Morphing via Orthogonal Box Drawings
(University of Waterloo, 20231218)Abstract: A graph is a set of vertices, with some pairwise connections given by a set of edges. A graph drawing, such as a nodelink diagram, visualizes a graph with geometric features. One of the most common forms of a ... 
List Coloring Some Classes of 1Planar Graphs
(University of Waterloo, 20211223)In list coloring we are given a graph G and a list assignment for G which assigns to each vertex of G a list of possible colors. We wish to find a coloring of the vertices of G such that each vertex uses a color from its ... 
Restricted String Representations
(University of Waterloo, 20170829)A string representation of a graph assigns to every vertex a curve in the plane so that two curves intersect if and only if the represented vertices are adjacent. This work investigates string representations of graphs ... 
Testing vertex connectivity of bowtie 1plane graphs
(University of Waterloo, 20220718)A separating set of a connected graph $G$ is a set of vertices $S$ such that $GS$ is disconnected. $S$ is a minimum separating set of $G$ if there is no separating set of $G$ with fewer vertices than $S$. The size of a ... 
Upward Octagonal Drawings of Ternary Trees
(University of Waterloo, 20160908)We explore ways to embed a ternary tree in an integer coordinate grid such that the width of the drawing is minimized. We provide upper and lower bounds on the width requirement of planar, straightline, upward, orderpreserving ...