Amanda Porter

Topic

Cops and Robbers on Edges, and Related Variants

Department of Mathematics and Statistics

Date & location

• Friday, August 14, 2026
• 12:30 P.M.
• Clearihue Building, Room B017

Examining Committee

Supervisory Committee

• Dr. Gary MacGillivray, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
• Dr. Melissa Huggan, Department of Mathematics and Statistics, UVic (Co-Supervisor)

External Examiner

• Dr. Nancy Clarke, Department of Mathematics and Statistics, Acadia University

Chair of Oral Examination

• Dr. Matt Moffitt, Department of Chemistry, UVic

Abstract

The game of Cops and Robbers is a two-player pursuit-evasion game played on a graph, in which a set of cops aims to capture a robber. The players occupy vertices of the graph, and capture occurs when at least one cop and the robber occupy the same vertex.

In this thesis, we consider a variant of Cops and Robbers where players occupy edges. We investigate the minimum number of cops required to capture the robber in a triangle-free graph by analyzing the structure of their associated line graphs. In doing so, we establish the edge cop number of triangle-free graphs is unbounded and characterize the triangle-free graphs that require only a single cop to capture the robber.

Additionally we discuss other variants of Cops and Robbers in which the cop and robber occupy a combination of vertices and edges. For all variants, we determine the minimum number of cops required to capture the robber on an 𝑛-dimensional hypercube to gain insight into how each variant’s rules impact the difficulty of capture.