This paper examines cop numbers and capture times in graphs, showing potential implications for asymmetric movement strategies.
We consider a variant of Cops and Robbers in which both the cops and the robber are allowed to traverse up to s edges on each of their turns, where s ≥ 2. We give several general for this new model as well as establish bounds for the cop numbers for grids and hypercubes. We also determine the capture time of cop-win graphs when $s = 2$ up to a small additive constant.
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Kinnersley et al. (2025) studied this question.
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