Computability Theoretic Results for the Game of Cops and Robbers on Infinite Graphs

Authors

Rachel D. Stahl, University of Connecticut - StorrsFollow

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