Computability Theoretic Results for the Game of Cops and Robbers on Infinite Graphs
Rachel D. Stahl · OpenCommons at University of Connecticut (University of Connecticut) · 2017
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.