Planar Capacitated Dominating Set Is W[1]-Hard

  title={Planar Capacitated Dominating Set Is W[1]-Hard},
  author={Hans L. Bodlaender and Daniel Lokshtanov and Eelko Penninkx},
Given a graph G together with a capacity function c : V (G) → N, we call S ⊆ V (G) a capacitated dominating set if there exists a mapping f : (V (G) \ S) → S which maps every vertex in (V (G) \S) to one of its neighbors such that the total number of vertices mapped by f to any vertex v ∈ S does not exceed c(v). In the Planar Capacitated Dominating Set problem we are given a planar graph G, a capacity function c and a positive integer k and asked whether G has a capacitated dominating set of… CONTINUE READING

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