Finding a vertex subset in a graph that satisfies a certain property is one of the most-studied topicsudin algorithmic graph theory. The focus herein is often on minimizing or maximizing the sizeudof the solution, that is, the size of the desired vertex set. In several applications, however, we alsoudwant to limit the “exposure” of the solution to the rest of the graph. This is the case, for example,udwhen the solution represents persons that ought to deal with sensitive information or a segregatedudcommunity. In this work, we thus explore the (parameterized) complexity of finding such secludedudvertex subsets for a wide variety of properties that they shall fulfill. More precisely, we study theudconstraint that the (open or closed) neighborhood of the solution shall be bounded by a parameterudand the influence of this constraint on the complexity of minimizing separators, feedback vertexudsets, F-free vertex deletion sets, dominating sets, and the maximization of independent sets.
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