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arXiv · 2607.21821

The 2-Cops-Move Cop Number of Graphs on the Torus, Klein Bottle, and Projective Plane

Florian Lehner·Alan Sun
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Abstract

We study the $2$-cops-move variant of the game of cops and robber, in which at most two cops may move in each turn. Let $c_2(G)$ denote the corresponding cop number. We prove that every graph embeddable on the torus, Klein bottle, or projective plane satisfies $c_2(G)\le 3$, extending a recent result of González Hermosillo de la Maza and Mohar for planar graphs.

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Florian Lehner, Alan Sun. 2026-07-23. The 2-Cops-Move Cop Number of Graphs on the Torus, Klein Bottle, and Projective Plane. https://arxiv.org/abs/2607.21821

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