Fully Active Cops and Robbers

TL;DR

This paper investigates a variation of the Cops and Robbers game where all agents must move each turn, analyzing how this rule affects the minimum number of cops needed across different graph classes.

Contribution

It introduces the Fully Active Cops and Robbers game, examining the impact of mandatory movement on pursuit strategies and cop number in various graph structures.

Findings

Mandatory movement increases the cop number in some graph classes.

Certain graph classes exhibit unchanged cop numbers despite the active movement rule.

Open problems are proposed for further exploration of the game's dynamics.

Abstract

We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum number of cops needed to catch the robber can change when this condition is added to the rules of the game. We study this `Fully Active Cops and Robbers' game for a number of classes of graphs and present some open problems for future research.