Seeing is not believing in limited visibility cops and robbers

TL;DR

This paper investigates the limited visibility Cops and Robbers game, showing that fewer cops are needed to see the robber than to capture him, and explores probabilistic approaches to approximate visibility with insufficient cops.

Contribution

It proves that the number of cops required for visibility can be arbitrarily less than for capture, addressing an open question, and examines probabilistic methods for partial visibility.

Findings

Number of cops needed for visibility can be arbitrarily smaller than for capture

Established a probabilistic framework for partial visibility scenarios

Answered an open question in the literature

Abstract

We consider the model of limited visibility Cops and Robbers, where the cops can only see within their $l$-neighbourhood. We prove that the number of cops needed to see the robber can be arbitrarily smaller than the number needed to capture the robber, answering an open question from the literature. We then consider how close we can get to seeing the robber when we do not have enough cops, along with a probabilistic interpretation.