Browsing University of Waterloo by Subject "planar graphs"

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Compact Routing on Planar Graphs

Seyedi, Newsha (University of Waterloo, 2024-01-04)

This thesis delves into the exploration of shortest path queries in planar graphs, with an emphasis on the utilization of space-efficient data structures. Our investigation primarily targets connected, undirected, static ...
Local Perspectives on Planar Colouring

Smith-Roberge, Evelyne (University of Waterloo, 2022-08-09)

In 1994, Thomassen famously proved that every planar graph is 5-choosable, resolving a conjecture initially posed by Vizing and, independently, Erdos, Rubin, and Taylor in the 1970s. Later, Thomassen proved that every ...
Shortest Paths in Geometric Intersection Graphs

Skrepetos, Dimitrios (University of Waterloo, 2018-06-29)

This thesis studies shortest paths in geometric intersection graphs, which can model, among others, ad-hoc communication and transportation networks. First, we consider two classical problems in the field of algorithms, ...
Transversal Problems In Sparse Graphs

Sun, Hao (University of Waterloo, 2022-09-20)

Graph transversals are a classical branch of graph algorithms. In such a problem, one seeks a minimum-weight subset of nodes in a node-weighted graph $G$ which intersects all copies of subgraphs~$F$ from a fixed family ...