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

It is known that the class of all graphs not containing a graph H as an induced subgraph is cop-bounded if and only if H is a forest whose every component is a path [4]. In this paper, we characterize all sets H of graphs with bounded diameter, such that H-free graphs are cop-bounded. This, in particular, gives a characterization of cop-bounded classes of graphs defined by a finite set of connected graphs as forbidden induced subgraphs. 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. (C) 2020 Elsevier B.V. All rights reserved.