Browsing Mathematics (Faculty of) by Supervisor "Biedl, Therese"
Now showing items 16 of 6

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, $\mathcal{R}_k(G)$, ... 
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 ... 
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 ...