Robber-monotonicity of bounded-speed visible active variants

Determine whether the bounded-speed visible active Cops-and-Robber copwidth variants have the robber-monotonicity property.

Background

The paper establishes several non-monotonicity results for bounded-speed Cops-and-Robber games, including failures of cop-monotonicity for visible active variants. However, the corresponding question for robber-monotonicity is not resolved. The conclusion explicitly identifies the robber-monotonicity of the bounded-speed visible active variants as an open question.

References

Furthermore, the robber-/monotonicity of both lazy copwidth variants for $s=2,3$ and the bounded speed visible active copwidth variants are open questions.

— Fast and Furious: A study on Monotonicity and Speed in Cops-and-Robber Games  (2502.15396 - Fluck et al., 21 Feb 2025) in Section 6, “Conclusion”