  The two-player, complete information game of Cops and Robber is played on
undirected finite graphs. A number of cops and one robber are positioned on
vertices and take turns in sliding along edges. The cops win if, after a move,
a cop and the robber are on the same vertex. The minimum number of cops needed
to catch the robber on a graph is called the cop number of that graph.
  In this paper, we study the cop number in the classes of graphs defined by
forbidding one or more graphs as either subgraphs or induced subgraphs. In the
case of a single forbidden graph we completely characterize (for both
relations) the graphs which force bounded cop number. En passant, we bound the
cop number in terms of tree-width.
