Composition of graphs and polyhedra II : Stable Sets

Barahona, Francisco; Mahjoub, Ali Ridha

Barahona, Francisco; Mahjoub, Ali Ridha (1994), Composition of graphs and polyhedra II : Stable Sets, SIAM Journal on Discrete Mathematics, 7, 3, p. 359-371. http://dx.doi.org/10.1137/S0895480190182678

Type

Article accepté pour publication ou publié

Date

1994

Journal name

SIAM Journal on Discrete Mathematics

Volume

Number

Publisher

Society for Industrial and Applied Mathematics

Pages

359-371

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

Subjects / Keywords

compact systems; stable set polytope; composition of polyhedra; polyhedral combinatorics