Cops and Robbers on Graphs with a Set of Forbidden Induced Subgraphs
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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. In this study, we characterize all sets H of graphs with some k∈N bounding the diameter of members of H from above, such that H-free graphs, i.e. graphs with no member of H as an induced subgraph, 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 there is k∈N bounding the diameter of components of members of H from above.
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