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Finding good 2-partitions of digraphs I. Hereditary properties

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Title: Finding good 2-partitions of digraphs I. Hereditary properties
Authors: Bang-Jensen, Jørgen, Havet, Frédéric
Contributors: Havet, Frederic
Source: Bang-Jensen, J & Havet, F 2016, ' Finding good 2-partitions of digraphs I. Hereditary properties ', Theoretical Computer Science, vol. 636, no. C, pp. 85-94 . https://doi.org/10.1016/j.tcs.2016.05.029
Publisher Information: Elsevier BV, 2016.
Publication Year: 2016
Subject Terms: polynomial, 0211 other engineering and technologies, 0102 computer and information sciences, 02 engineering and technology, Out-branching, Polynomial, semicomplete digraph, 01 natural sciences, out-branching, splitting digraphs, Feedback vertex set, Acyclic, minimum degree, NP-complete, Semicomplete digraph, oriented, 2-partition, acyclic, Oriented, feedback vertex set, partition, tournament, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Minimum degree, Splitting digraphs, Tournament, Partition
Description: 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 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 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 problems when both P1 and P2 are in E is determined in the companion paper [2].
Document Type: Article
File Description: application/pdf
Language: English
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.05.029
Access URL: https://hal.archives-ouvertes.fr/hal-01327015/document
https://www.sciencedirect.com/science/article/pii/S0304397516301657
https://dblp.uni-trier.de/db/journals/tcs/tcs636.html#Bang-JensenH16
https://hal.inria.fr/hal-01279332
http://findresearcher.sdu.dk/portal/en/publications/finding-good-2partitions-of-digraphs-i-hereditary-properties(73b657c3-d3b4-4a34-805d-dd14824b7776).html
https://hal.archives-ouvertes.fr/hal-01327015
https://portal.findresearcher.sdu.dk/da/publications/73b657c3-d3b4-4a34-805d-dd14824b7776
https://portal.findresearcher.sdu.dk/da/publications/73b657c3-d3b4-4a34-805d-dd14824b7776
https://doi.org/10.1016/j.tcs.2016.05.029
Rights: Elsevier Non-Commercial
Accession Number: edsair.doi.dedup.....296f0ac2c6e8ccb49eb94c50d6ac1780
Database: OpenAIRE
Description
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 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 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 problems when both P1 and P2 are in E is determined in the companion paper [2].
ISSN:03043975
DOI:10.1016/j.tcs.2016.05.029