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On the maximum independent set problem in subclasses of subcubic graphs

Ries, Bernard; Monnot, Jérôme; Lozin, Vadim (2015), On the maximum independent set problem in subclasses of subcubic graphs, Journal of Discrete Algorithms, 31, p. 104-112. 10.1016/j.jda.2014.08.005

Type
Article accepté pour publication ou publié
Date
2015
Journal name
Journal of Discrete Algorithms
Volume
31
Publisher
Elsevier
Pages
104-112
Publication identifier
Metadata
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Author(s)
Ries, Bernard
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Monnot, Jérôme cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lozin, Vadim
Warwick Mathematics Institute and DIMAP
Abstract (EN)
It is known that the maximum independent set problem is NP-complete for subcubic graphs, i.e. graphs of vertex degree at most 3. Moreover, the problem is NP-complete for 3-regular Hamiltonian graphs and for H -free subcubic graphs whenever H contains a connected component which is not a tree with at most 3 leaves. We show that if every connected component of H is a tree with at most 3 leaves and at most 7 vertices, then the problem can be solved for H -free subcubic graphs in polynomial time. We also strengthen the NP-completeness of the problem on 3-regular Hamiltonian graphs by showing that the problem is APX-complete in this class
Subjects / Keywords
APX-completeness; Subcubic graph; Polynomial-time algorithm; Independent set