Now showing items 1-7 of 7

• #### A 2-Approximation for the Height of Maximal Outerplanar Graph Drawings ﻿

(University of Waterloo, 2016-08-18)
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 ...
• #### Area-Efficient Drawings of Outer-1-Planar Graphs ﻿

(University of Waterloo, 2020-09-29)
We study area-efficient 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 outer-1-planar graphs: the family of planar ...
• #### Bounds on Maximum Matchings in 1-Planar Graphs ﻿

(University of Waterloo, 2019-01-29)
In this thesis, we study lower bounds on maximum matchings in 1-planar 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, 2020-05-13)
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, $\mathcal{R}_k(G)$, ...
• #### List Coloring Some Classes of 1-Planar Graphs ﻿

(University of Waterloo, 2021-12-23)
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, 2017-08-29)
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, 2016-09-08)
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, straight-line, upward, order-preserving ...

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