On the parameterized complexity of 2-partitions

Jonas Bamse Andersen; Jørgen Bang-Jensen; Anders Yeo

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arXiv · 2003.07190

On the parameterized complexity of 2-partitions

Jonas Bamse Andersen·Jørgen Bang-Jensen·Anders Yeo

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Abstract

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 $|V_i|\geq k_i$, where $k_1,k_2$ are part of the input. This settles an open problem from[1,4].

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Jonas Bamse Andersen, Jørgen Bang-Jensen, Anders Yeo. 2020-03-16. On the parameterized complexity of 2-partitions. https://arxiv.org/abs/2003.07190

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