We present a new exact approach to the stable set problem, which avoids the pitfalls of existing approaches based on linear and semidefinite programming. The main idea is to construct an ellipsoid which contains the stable set polytope, in such a way that the upper bound obtained by optimising over the ellipsoid is equal to the Lovasz theta number. This ellipsoid can then be used to construct useful convex programming relaxations of the stable set problem or, more interestingly, to derive cutting planes. These cutting planes turn out to be remarkably strong and easy to generate.
This was eventually published as: M. Giandomenico, A.N. Letchford, F. Rossi & S. Smriglio (2011) An new approach to the stable set problem based on ellipsoids. In O. Günlük & G.J. Woeginger (eds.) Integer Programming and Combinatorial Optimization XV. Lecture Notes in Computer Science, vol. 6655. Heidelberg: Springer.