Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

William Kinnersley


This dissertation presents two variants of Cops and Robbers that feature asymmetric movement, meaning that the cops and robber have different rules for traversing the edges of the graph. The first variant discussed is the bridge-burning variant, wherein the game is played on an undirected graph and the robber deletes any edge he traverses. The second variant discussed is the weak directed variant, wherein the game is played on a directed graph; here the cops can only move along each edge in the direction it points, whereas the robber can traverse each edge in either direction. In both variants, we will be looking at the cop numbers for well-known classes of graphs.



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