On the Maximum Independent Set Problem in Subclasses of Subcubic Graphs

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

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

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 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.

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

Domaines: Informatique [cs]

Vadim Lozin, Jérôme Monnot, Bernard Ries. On the Maximum Independent Set Problem in Subclasses of Subcubic Graphs. 24th International Workshop, IWOCA 2013, Jul 2013, Rouen, France. pp.314-326, ⟨10.1007/978-3-642-45278-9_27⟩. ⟨hal-01616215⟩