Date
1994
Dewey
Principes généraux des mathématiques
Sujet
compact systems; stable set polytope; composition of polyhedra; polyhedral combinatorics
Journal issue
SIAM Journal on Discrete Mathematics
Volume
7
Number
3
Publication date
1994
Article pages
359-371
Publisher
Society for Industrial and Applied Mathematics
Author
Barahona, Francisco
Mahjoub, Ali Ridha
Type
Article accepté pour publication ou publié
Abstract (EN)
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