Graph searching in a crime wave

We define helicopter cop and robber games with multiple robbers, extending previous research, which only considered the pursuit of a single robber. Our model is defined for robbers that are visible (the cops know their position) and active (able to move at every turn) but is easily adapted to other common variants of the game. The game with many robbers is non-monotone: more cops are needed if their moves are restricted so as to monotonically decrease the space available to the robbers. Because the cops may decide their moves based on the robbers' current position, strategies in the game are interactive but the game becomes, in a sense, less interactive as the initial number of robbers increases. We prove that the main parameter emerging from the game captures a hierarchy of parameters between proper pathwidth and proper treewidth. We give a complete characterization of the parameter for trees and an upper bound for general graphs.