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arXiv · 2511.22278

Blind cop-width and balanced minors of graphs

Hector Buffière·Rutger Campbell·Kevin Hendrey·Sang-il Oum
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Abstract

We investigate a pursuit-evasion game on an undirected graph in which a robber, moving at a fixed constant speed, attempts to evade a team of cops who are blind to the robber's location and can quickly travel between any pair of vertices in the graph. The blind cop-width is the minimum number of cops needed to catch the robber on a given graph. We link it with other known graph parameters defined in terms of pursuit-evasion games, and show a new lower bound with respect to treewidth. The proof introduces the notion of balanced minors, where all branch sets of a minor model have equal size.

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Hector Buffière, Rutger Campbell, Kevin Hendrey, Sang-il Oum. 2025-11-27. Blind cop-width and balanced minors of graphs. https://arxiv.org/abs/2511.22278

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