Preprint / Version 0

Blind cop-width and balanced minors of graphs

Authors

  • Hector Buffière
  • Rutger Campbell
  • Kevin Hendrey
  • Sang-il Oum

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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Posted

2025-11-27