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Finding Secluded Places of Special Interest in Graphs

Till Fluschnik (TU Berlin)


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.

This is joint work with René van Bevern, George B. Mertzios, Hendrik Molter, Manuel Sorge, and
Ondřej Suchý.



Till Fluschnik
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