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

2026/07/23 by Florian Lehner, Alan Sun
#math.CO

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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 c₂(G) denote the corresponding cop number. We prove that every graph embeddable on the torus, Klein bottle, or projective plane satisfies c₂(G)≤ 3, extending a recent result of González Hermosillo de la Maza and Mohar for planar graphs.

Citations

• Vertex-to-vertex pursuit in a graph

Related

• The Cops & Robber game on series-parallel graphs
• The Cop Number of the One-Cop-Moves Game on Planar Graphs
• Cops and robbers on planar directed graphs
• Cop number of graphs without long holes
• Cops and Attacking Robbers with Cycle Constraints