Browsing Mathematics (Faculty of) by Supervisor "Biedl, Therese"
Now showing items 1-6 of 6
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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, $\mathcal{R}_k(G)$, ... -
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 ...