Abstract
We study several problems of clearing subgraphs by mobile agents in digraphs. The agents can move only along directed walks of a digraph and, depending on the variant, their initial positions may be pre-specified. In general, for a given subset \(\mathcal {S}\) of vertices of a digraph D and a positive integer k, the objective is to determine whether there is a subgraph \(H=(\mathcal {V}_H,\mathcal {A}_H)\) of D such that (a) \(\mathcal {S}\subseteq \mathcal {V}_H\), (b) H is the union of k directed walks in D, and (c) the underlying graph of H includes a Steiner tree for \(\mathcal {S}\). We provide several results on parameterized complexity and hardness of the problems.
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