On the maximum independent set problem in subclasses of subcubic graphs

Bernard Ries (1) , Jérôme Monnot (1) , Vadim Lozin (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 Warwick Mathematics Institute and DIMAP

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

Mots clés: APX-completeness; Subcubic graph; Polynomial-time algorithm; Independent set

Domaines: Informatique [cs]

Bernard Ries, Jérôme Monnot, Vadim Lozin. On the maximum independent set problem in subclasses of subcubic graphs. Journal of Discrete Algorithms, 2015, 31, ⟨10.1016/j.jda.2014.08.005⟩. ⟨hal-01508780⟩