Date of Completion
5-4-2017
Embargo Period
5-4-2017
Major Advisor
Dr. David Reed Solomon
Associate Advisor
Dr. Damir Dzhafarov
Associate Advisor
Dr. Tom Roby
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
Several results about the game of cops and robbers on infinite graphs are analyzed from the perspective of computability theory and reverse mathematics. Computable robber-win graphs are constructed with the property that no computable robber strategy is a winning strategy, and such that for an arbitrary computable ordinal n, any winning strategy has complexity at least 0(n). Symmetrically, computable cop-win graphs are constructed with the property that no computable cop strategy is a winning strategy. However the coding methods used in the robber-win case fail here. Locally finite infinite trees and graphs are explored using tools of reverse mathematics. The Turing computability of a binary relation used to classify cop-win graphs is studied.
Recommended Citation
Stahl, Rachel D., "Computability Theoretic Results for the Game of Cops and Robbers on Infinite Graphs" (2017). Doctoral Dissertations. 1463.
https://digitalcommons.lib.uconn.edu/dissertations/1463