Accelerated Cops and Robbers

Published 25 Jun 2025 in math.CO and cs.DM | (2506.20753v1)

Abstract: 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 $s \ge 2$. 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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