Abstract
We study the complexity of deciding whether a given digraph D has a vertex-partition into two disjoint subdigraphs with given structural properties. Let H and E denote the following two sets of natural properties of digraphs: H = {acyclic, complete, arcless, oriented (no 2-cycle), semicomplete, symmetric, tournament} and E = {strongly connected, connected, minimum out-degree at least 1, minimum in-degree at least 1, minimum semi-degree at least 1, minimum degree at least 1, having an out-branching, having an in-branching}. In this paper, we determine the complexity of deciding, for any fixed pair of positive integers k1,k2, whether a given digraph has a vertex partition into two digraphs D1,D2 such that |V(Di)|≥ki and Di has property Pi for i=1,2 when P1∈H and P2∈H∪E. We also classify the complexity of the same problems when restricted to strongly connected digraphs.The complexity of the 2-partition problems where both P1 and P2 are in E is determined in the companion paper [2].
Published Version
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