On the use of Boolean methods for the computation of the stability number Original Research Article

We study a transformation of pseudo-Boolean functions which, when applicable, amounts to constructing from a graph G = (V, E) a new graph Gʹ = (Vʹ, Eʹ) with the same stability number and such that ¦V ʹ ¦= ¦V ¦ − 1. This transformation provides a polynomial time algorithm for the computation of the stability number of graphs which contain neither an induced chordless cycle with four vertices, nor its complement. The transformation might also be useful for reducing the size of a claw-free graph while preserving its stability number.