On the complexity of computing the $k$-restricted edge-connectivity of a graph

2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing $\lambda_k(G)$. Very recently, in the parameterized complexity community the notion of \emph{good edge separation} of a graph has been defined, which happens to be essentially the same as the $k$-restricted edge-connectivity. Motivated by the relevance of this invariant from both combinatorial and algorithmic points of view, in this article we initiate a systematic study of its computational complexity, with special emphasis on its parameterized complexity for several choices of the parameters. We provide a number of NP-hardness and W[1]-hardness results, as well as FPT-algorithms.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01272707
Contributor : Ignasi Sau <>
Submitted on : Thursday, February 11, 2016 - 11:58:01 AM
Last modification on : Tuesday, December 17, 2019 - 10:00:03 AM

Identifiers

• HAL Id : lirmm-01272707, version 1
• ARXIV : 1502.07659

Citation

Luis Pedro Montejano, Ignasi Sau Valls. On the complexity of computing the $k$-restricted edge-connectivity of a graph. 2016. ⟨lirmm-01272707⟩

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