Cops and robbers on geometric graphs and graphs with a set of forbidden subgraphs

In this thesis we study the game of cops and robbers on some special class of graphs, including planar graphs and geometric graphs. Moreover, under some conditions on graph diameter, we characterize all sets H of graphs with bounded diameter for which H-free graphs are cop-bounded. Furthermore, we extend our characterization to the case of cop-bounded classes of graphs defined by a set H of forbidden graphs such that the components of members of H have bounded diameter.