On the Existence and Determination of Satisfactory Partitions in a Graph

Abstract

The Satisfactory Partition problem consists in deciding if a given graph has a partition of its vertex set into two nonempty sets V ₁,V ₂ such that for each vertex v, if v ∈ V _i then $d_{V_i}(v) \geq s(v)$, where s(v)≤ d(v) is a given integer-valued function. This problem was introduced by Gerber and Kobler [EJOR 125 (2000), 283–291] for $s = \lceil \frac{d}{2} \rceil$. In this paper we study the complexity of this problem for different values of s.