The game of Ambush Cops and Robbers played on chordal graphs and outerplanar graphs
Introduced concurrently by Nowakowski \& Winkler and Quilliot, the game of Cops and Robber is a turn based vertex-to-vertex pursuit evasion game played on graphs. Generally, researchers are concerned in optimizing the amount of resources used in capturing the robber. That is, one often seeks to use as few cops and/or turns as possible in the execution of a winning strategy. Since its introduction, much progress has been made on the original problem thus leading to the introduction of multiple variations; in said variations, constraints are usually imposed on the cops' movements or visibility. In this talk, we examine one such variation dubbed the game of Ambush Cops and Robbers. This particular game is played with two robbers that are given the power to ambush a cop. They may do so by both moving to the same vertex as said cop, hereby winning the game. Otherwise, rules of this variation follow those of the game of Cops and Robber. Much of the existing research focusses on characterizing graphs on which a single cop has an ambush-winning strategy. A natural direction is to investigate classes of graphs for which multiple cops are needed. We shall present our results on two particular classes of graphs: chordal graphs and outerplanar graphs. This is joint work with Dr. Nancy Clarke.