Perfect stables in graphs

A perfect stable in a graph G is a stable S with the property that any vertex of G is either in S or adjacent with at least two vertices which are in S. This concept is an obvious generalization of the notion of perfect matching. In this note, the problem of deciding if a given graph has a perfect stable is considered. This problem is shown to be in general NP-complete, but polynomial for K_1,3-free graphs.