## Abstract

We continue the study, initiated in [3], of the complexity of deciding whether a given digraph D has a vertex-partition into two disjoint subdigraphs with given structural properties and given minimum cardinality. Let E be the following set of properties of digraphs: 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, for all choices of P
_{1},P
_{2} from E and all pairs of fixed positive integers k
_{1},k
_{2}, the complexity of deciding whether a digraph has a vertex partition into two digraphs D
_{1},D
_{2} such that D
_{i} has property P
_{i} and |V(D
_{i})|≥k
_{i}, i=1,2. We also classify the complexity of the same problems when restricted to strongly connected digraphs. The complexity of the analogous problems when P
_{1}∈H and P
_{2}∈H∪E, where H={acyclic, complete, arc-less, oriented (no 2-cycle), semicomplete, symmetric, tournament} were completely characterized in [3].

Original language | English |
---|---|

Journal | Theoretical Computer Science |

Volume | 640 |

Pages (from-to) | 1-19 |

ISSN | 0304-3975 |

DOIs | |

Publication status | Published - 2016 |

## Keywords

- 2-Partition
- Acyclic
- Feedback vertex set
- Minimum degree
- NP-complete
- Oriented
- Out-branching
- Partition
- Polynomial
- Semicomplete digraph
- Splitting digraphs
- Tournament