Complexity of the satisfactory partition problem

Cristina Bazgan (1) , Zsolt Tuza (2) , Daniel Vanderpooten (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 MTA SZTAKI - Computer and Automation Research Institute [Budapest]

The SATISFACTION PARTITION problem consists in deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other parts. This problem was introduced by Gerber enad Kobler [GK98, GK00] and further studied by other authors but its complexity remained open until now. We also study generalizations and variants of this problem where a partition into K nonempty parts (K>ou =3) is requested.

Mots clés: Satisfactory partition; graph; complexity; polynomial algorithm; NP-complete

Domaines: Complexité [cs.CC]; Mathématique discrète [cs.DM]

Cristina Bazgan, Zsolt Tuza, Daniel Vanderpooten. Complexity of the satisfactory partition problem. 2005. ⟨hal-00004258⟩