  We propose general separation procedures for generating cuts for the stable
set polytope, inspired by a procedure by Rossi and Smriglio and applying a
lifting method by Xavier and Camp\^{e}lo. In contrast to existing
cut-generating procedures, ours generate both rank and non-rank valid
inequalities, hence they are of a more general nature than existing methods.
This is accomplished by iteratively solving a lifting problem, which consists
of a maximum weighted stable set problem on a smaller graph. Computational
experience on DIMACS benchmark instances shows that the proposed approach may
be a useful tool for generating cuts for the stable set polytope.
