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Disjoint Paths in Decomposable Digraphs

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Název: Disjoint Paths in Decomposable Digraphs
Autoři: Bang-Jensen, Jørgen, Christiansen, Tilde My, Maddaloni, Alessandro
Zdroj: Bang-Jensen, J, Christiansen, T M & Maddaloni, A 2017, ' Disjoint paths in decomposable digraphs ', Journal of Graph Theory, vol. 85, no. 2, pp. 545-567 . https://doi.org/10.1002/jgt.22090
Informace o vydavateli: Wiley, 2016.
Rok vydání: 2016
Témata: disjoint paths, k-linkage problem, quasi-transitive digraph, polynomial algorithm, 0102 computer and information sciences, (round-)decomposable digraphs, locally semicomplete digraph, 01 natural sciences
Popis: The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].
Druh dokumentu: Article
Jazyk: English
ISSN: 1097-0118
0364-9024
DOI: 10.1002/jgt.22090
Přístupová URL adresa: https://portal.findresearcher.sdu.dk/da/publications/993feb05-2974-4b25-a9e2-8b278a99554b
https://portal.findresearcher.sdu.dk/da/publications/993feb05-2974-4b25-a9e2-8b278a99554b
https://doi.org/10.1002/jgt.22090
Rights: Wiley Online Library User Agreement
Přístupové číslo: edsair.doi.dedup.....44b9f5553c467716dce576e52797a7b7
Databáze: OpenAIRE
Popis
Abstrakt:The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].
ISSN:10970118
03649024
DOI:10.1002/jgt.22090