René van Bevern, Till Fluschnik, George B. Mertzios, Hendrik Molter, Manuel Sorge, and Ondřej Suchý. Finding secluded places of special interest in graphs. In Proceedings of the 11th International Symposium on Parameterized and Exact Computation (IPEC'16), Aarhus, Denmark, volume 63 of Leibniz International Proceedings in Informatics (LIPIcs), pages 5:1–5:16. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2017.

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

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