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

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.

Figures (1)

• Figure 1: Alternating strategy on grid, knowledgeable agent is blue and ignorant red

Theorems & Definitions (37)

• Definition 1
• Theorem 2: DGLM20
• Theorem 3: DGLM20
• Theorem 4: DGLM20
• Theorem 5: MRS25
• Lemma 6
• proof
• Corollary 7: Theorem \ref{['the:cycle']}
• Corollary 8: Theorem \ref{['the:alg-works']}
• Theorem 9