Broadcasting Agents and Adversary: A new variation on Cops and Robbers

TL;DR

This paper introduces a new graph game called 'Agents and Adversary', classifies graph families by winning strategies, and establishes bounds on agents' time-to-win, offering insights into graph symmetry and strategy.

Contribution

It presents a novel variation of the Cops and Robbers game, defines new graph symmetry concepts, and provides bounds for agents' winning times on infinite graph families.

Findings

Classified infinite graph families as Agents-win or Adversary-win

Defined a new graph symmetry related to winning strategies

Established tight bounds on agents' time-to-win

Abstract

We introduce a new game played on graphs, ``Agents and Adversary". This game is reminiscent of ``Cops and Robbers" but has some fundamental differences. We classify infinite families of graphs as Agents-win and Adversary-win. We then define a new type of graph symmetry and use it to define a winning strategy for Adversary. Finally, we give tight upper and lower bounds for Agents' time-to-win on several infinite families of graphs.