Compositions of Graphs and Polyhedra II: Stable Sets
Francisco Barahona, Ali Ridha Mahjoub · SIAM Journal on Discrete Mathematics · 1994
A graph G with a two-node cutset decomposes into two pieces. A technique to describe the stable set polytope for G based on stable set polytopes associated with the pieces is studied. This gives a way to characterize this polytope for classes of graphs that can be recursively decomposed. This also gives a procedure to describe new facets of this polytope. A compact system for the stable set problem in series-parallel graphs is derived. This technique is also applied to characterize facet-defining inequalities for graphs with no $K_5 \backslash e$ minor. The stable set problem is polynomially solvable for this class of graphs. Compositions of h-perfect graphs are also studied.