Elsevier

Theoretical Computer Science

Volume 640, 9 August 2016, Pages 1-19
Theoretical Computer Science

Finding good 2-partitions of digraphs II. Enumerable properties

https://doi.org/10.1016/j.tcs.2016.05.034Get rights and content
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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 P1,P2 from E and all pairs of fixed positive integers k1,k2, the complexity of deciding whether a digraph has a vertex partition into two digraphs D1,D2 such that Di has property Pi and |V(Di)|ki, 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 P1H and P2HE, where H={acyclic, complete, arc-less, oriented (no 2-cycle), semicomplete, symmetric, tournament} were completely characterized in [3].

Keywords

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

Cited by (0)

1

This work was done while the first author was visiting INRIA, Sophia Antipolis, France, project COATI. Hospitality and financial support from Labex UCN@Sophia, Sophia Antipolis is gratefully acknowledged. The research of Bang-Jensen was also supported by the Danish research council under grant number 1323-00178B.

2

Partially supported by ANR under contract STINT ANR-13-BS02-0007.