Galli, Laura and Letchford, Adam Nicholas (2017) On the Lovász theta function and some variants. Discrete Optimization, 25. pp. 159-174. ISSN 1572-5286
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Abstract
The Lovász theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovász and the other to Gr�ötschel et al. The former SDP is often thought to be preferable computationally, since it has fewer variables and constraints. We derive some new results on these two equivalent SDPs. The surprising result is that, if we weaken the SDPs by aggregating constraints, or strengthen them by adding cutting planes, the equivalence breaks down. In particular, the Gr�ötschel et al. scheme typically yields a stronger bound than the Lovász one.