Game of zero-visibility cops and robber is a two-player game played on a connected graph in which the cops have no information about the robber’s location, while the omniscient robber knows both the cops’ positions and their strategy. This thesis examines the optimization problem of determining the zero-visibility cop number, that is, the minimum number of cops required to guarantee the robber’s capture. We present optimal winning strategies for the cops on selected basic graph families, trees, and general graphs. For general graphs, we derive an upper bound on the zero-visibility cop number using path decompositions and the pathwidth of a graph.
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