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

The k-restricted edge-connectivity of a graph G, denoted by λk(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 exte...

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Bibliographic Details
Published in:Theoretical computer science Vol. 662; pp. 31 - 39
Main Authors: Montejano, Luis Pedro, Sau, Ignasi
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2017
Elsevier
Subjects:
Algorithms
Combinatorial analysis
Communities
Complexity
Computation
FPT-algorithm
Good edge separation
Graph cut
Graph theory
Graphs
Invariants
k-Restricted edge-connectivity
Mathematics
Parameterized complexity
Polynomial kernel
Good edge separation
Graph cut
k-Restricted edge-connectivity
Polynomial kernel
Parameterized complexity
FPT-algorithm
k-restricted edge-connectivity
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:The k-restricted edge-connectivity of a graph G, denoted by λk(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 λk(G). Very recently, in the parameterized complexity community the notion of 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.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.12.006