Academic Journal
Complexity results on the decomposition of a digraph into directed linear forests and out-stars
| Τίτλος: | Complexity results on the decomposition of a digraph into directed linear forests and out-stars |
|---|---|
| Συγγραφείς: | Hörsch, Florian, Picasarri-Arrieta, Lucas |
| Συνεισφορές: | Helmholtz Center for Information Security Saarbrücken (CISPA), Combinatorics, Optimization and Algorithms for Telecommunications (COATI), Centre Inria d'Université Côte d'Azur, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA), National Institute of Informatics (NII), ANR-19-CE48-0013,DIGRAPHS,Digraphes(2019), ANR-17-EURE-0004,UCA DS4H,UCA Systèmes Numériques pour l'Homme(2017) |
| Πηγή: | EISSN: 1077-8926 ; The Electronic Journal of Combinatorics ; https://inria.hal.science/hal-04471664 ; The Electronic Journal of Combinatorics, 2024, 31 (P4.26), pp.40 |
| Στοιχεία εκδότη: | CCSD Open Journal Systems |
| Έτος έκδοσης: | 2024 |
| Συλλογή: | HAL Université Côte d'Azur |
| Θεματικοί όροι: | complexity, directed stars, directed linear forests, branchings, arboricity, arc-partitions, Digraphs, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] |
| Περιγραφή: | International audience ; We consider two decomposition problems in directed graphs. We say that a digraph is $k$-bounded for some $k \in \mathbb{Z}_{\geq 1}$ if each of its connected components contains at most $k$ arcs. For the first problem, a directed linear forest is a collection of vertex-disjoint directed paths and we consider the problem of decomposing a given digraph into a $k$-bounded and an $\ell$-bounded directed linear forest for some fixed $k,\ell \in \mathbb{Z}_{\geq 1}\cup \{\infty\}$. We give a full dichotomy for this problem by showing that it can be solved in polynomial time if $k+\ell \leq 3$ and is NP-complete otherwise. This answers a question of Campbell, H\"orsch, and Moore. For the second problem, we say that an out-galaxy is a vertex-disjoint collection of out-stars. Again, we give a full dichotomy of when a given digraph can be edge-decomposed into a $k$-bounded and an $\ell$-bounded out-galaxy for fixed $k,\ell \in \mathbb{Z}_{\geq 1}\cup \{\infty\}$. More precisely, we show that the problem can be solved in polynomial time if $\min\{k,\ell\}\in \{1,\infty\}$ and is NP-complete otherwise. |
| Τύπος εγγράφου: | article in journal/newspaper |
| Γλώσσα: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2401.09202; ARXIV: 2401.09202 |
| Διαθεσιμότητα: | https://inria.hal.science/hal-04471664 https://inria.hal.science/hal-04471664v2/document https://inria.hal.science/hal-04471664v2/file/2401.09202v2.pdf |
| Rights: | https://creativecommons.org/licenses/by/4.0/ ; info:eu-repo/semantics/OpenAccess |
| Αριθμός Καταχώρησης: | edsbas.1440F37 |
| Βάση Δεδομένων: | BASE |
| Η περιγραφή δεν είναι διαθέσιμη |