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Finding good 2-partitions of digraphs II. Enumerable properties

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Title: Finding good 2-partitions of digraphs II. Enumerable properties
Authors: Bang-Jensen, Jørgen, Cohen, Nathann, Havet, Frédéric
Contributors: Cohen, Nathann
Source: Bang-Jensen, J, Cohen, N & Havet, F 2016, ' Finding good 2-partitions of digraphs II. Enumerable properties ', Theoretical Computer Science, vol. 640, pp. 1-19 . https://doi.org/10.1016/j.tcs.2016.05.034
Publisher Information: Elsevier BV, 2016.
Publication Year: 2016
Subject Terms: Semicomplete digraph, 0211 other engineering and technologies, Oriented, [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0102 computer and information sciences, 02 engineering and technology, Out-branching, Polynomial, 01 natural sciences, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], 2-Partition, Minimum degree, [INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC], Tournament, Feedback vertex set, Splitting digraphs, Acyclic, Partition, NP-complete
Description: 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 EE be the following set of properties of digraphs: E=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,P2P1,P2 from EE and all pairs of fixed positive integers k1,k2k1,k2, the complexity of deciding whether a digraph has a vertex partition into two digraphs D1,D2D1,D2 such that DiDi has property PiPi and |V(Di)|≥ki|V(Di)|≥ki, i=1,2i=1,2. We also classify the complexity of the same problems when restricted to strongly connected digraphs. The complexity of the analogous problems when P1∈HP1∈H and P2∈H∪EP2∈H∪E, where H=H={acyclic, complete, arc-less, oriented (no 2-cycle), semicomplete, symmetric, tournament} were completely characterized in [3].
Document Type: Article
File Description: application/pdf
Language: English
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.05.034
Access URL: https://www.sciencedirect.com/science/article/pii/S0304397516301815
https://dblp.uni-trier.de/db/journals/tcs/tcs640.html#Bang-JensenCH16
https://hal.archives-ouvertes.fr/hal-01346079
https://hal.inria.fr/hal-01279338
https://hal.archives-ouvertes.fr/hal-01346079/document
https://hal.inria.fr/hal-01279338/document
https://portal.findresearcher.sdu.dk/da/publications/d35f3f3c-e4dc-43c9-9237-62a0f13a963b
Rights: Elsevier Non-Commercial
Accession Number: edsair.doi.dedup.....125940c4c2f53d2b0f367c2e6385e90c
Database: OpenAIRE
Description
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 EE be the following set of properties of digraphs: E=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,P2P1,P2 from EE and all pairs of fixed positive integers k1,k2k1,k2, the complexity of deciding whether a digraph has a vertex partition into two digraphs D1,D2D1,D2 such that DiDi has property PiPi and |V(Di)|≥ki|V(Di)|≥ki, i=1,2i=1,2. We also classify the complexity of the same problems when restricted to strongly connected digraphs. The complexity of the analogous problems when P1∈HP1∈H and P2∈H∪EP2∈H∪E, where H=H={acyclic, complete, arc-less, oriented (no 2-cycle), semicomplete, symmetric, tournament} were completely characterized in [3].
ISSN:03043975
DOI:10.1016/j.tcs.2016.05.034