A main result of combinatorial optimization is that the clique and chromatic numbers of a
perfect graph are computable in polynomial time (Grötschel et al., 1981)[7]. This result relies
on polyhedral characterizations of perfect graphs involving the stable set polytope of the
graph, a linear relaxation defined by clique constraints, and a semi-definite relaxation, the
Theta-body of the graph. A natural question is whether the algorithmic results for perfect
graphs can be extended to graph classes with similar polyhedral properties. We consider a …

A main result of combinatorial optimization is that clique and chromatic number of a perfect
graph are computable in polynomial time (Grötschel, Lovász and Schrijver 1981). This result
relies on polyhedral characterizations of perfect graphs involving the stable set polytope of
the graph, a linear relaxation defined by clique constraints, and a semi-definite relaxation,
the Theta-body of the graph. A natural question is whether the algorithmic results for perfect
graphs can be extended to graph classes with similar polyhedral properties. We consider a …