Published April 2018
| Version v1
Journal article
Finding a subdivision of a prescribed digraph of order 4
Contributors
Others:
- Combinatorics, Optimization and Algorithms for Telecommunications (COATI) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; 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) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
- Parallelism, Graphs and Optimization Research Group (ParGO) ; Universidade Federal do Ceará = Federal University of Ceará (UFC)
- Department of Mathematics [Burnaby] (SFU) ; Simon Fraser University (SFU.ca)
- CAPES/Brazil
- Research Grant P1–0297 of ARRS
- NSERC Discovery Grant
- Canada Research Chair program
- ANR-13-BS02-0007,Stint,Structures Interdites(2013)
Description
The problem of when a given digraph contains a subdivision of a fixed digraph F is considered. Bang-Jensen et al. [2] laid out foundations for approaching this problem from the algorith-mic point of view. In this paper we give further support to several open conjectures and speculations about algorithmic complexity of finding F-subdivisions. In particular, up to 5 exceptions, we completely classify for which 4-vertex digraphs F , the F-subdivision problem is polynomial-time solvable and for which it is NP-complete. While all NP-hardness proofs are made by reduction from some version of the 2-linkage problem in digraphs, some of the polynomial-time solvable cases involve relatively complicated algorithms.
Abstract
International audienceAdditional details
Identifiers
- URL
- https://hal.inria.fr/hal-01711403
- URN
- urn:oai:HAL:hal-01711403v1
Origin repository
- Origin repository
- UNICA