Struction revisited

AbstractThe struction method is a general approach to compute the stability number of a graph based on step-by-step transformations each of which reduces the stability number by exactly one. This approach has been originally derived from Boolean arguments and has been applied by different authors to compute in polynomial time the stability number in special classes of graphs. In the present paper we review basic results on this topic and propose a generalization of the struction. We also discuss its relationship with some other graph transformations, such as the cycle shrinking of Edmonds or the clique reduction of Lovász–Plummer, and the possibility to use stability preserving transformations to increase the efficiency of this approach