On the parameterized complexity of 2-partitions
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We give an FPT algorithm for deciding whether the vertex set a digraph D can be partitioned into two disjoint sets V_1,V_2 such that the digraph D[V_1] induced by V_1 has a vertex that can reach all other vertices by directed paths, the digraph D[V_2] has no vertex of in-degree zero and |V_i|≥ k_i, where k_1,k_2 are part of the input. This settles an open problem from[1,4].
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