Elsevier

Theoretical Computer Science

Volume 636, 11 July 2016, Pages 85-94
Theoretical Computer Science

Finding good 2-partitions of digraphs I. Hereditary properties

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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 P1H and P2HE. 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].

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 project COATI (I3S and INRIA), Sophia Antipolis, France. 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.