TWO VARIANTS OF COPS AND ROBBERS WITH ASYMMETRIC MOVEMENT RULES

Author

Eric Peterson, University of Rhode IslandFollow

Date of Award

2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

William Kinnersley

Abstract

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.

Recommended Citation

Peterson, Eric, "TWO VARIANTS OF COPS AND ROBBERS WITH ASYMMETRIC MOVEMENT RULES" (2020). Open Access Dissertations. Paper 1156.
https://digitalcommons.uri.edu/oa_diss/1156