Adding cuts based on copositive matrices, we propose to improve Lovász' bound on the clique number and its tightening introduced by McEliece, Rodemich, Rumsey, and Schrijver. Candidates for cheap and efficient copositivity cuts of this type are obtained from graphs with known clique number. The cost of previously established semidefinite programming bound hierarchies rapidly increases with the order (and quality requirements). By contrast, the bounds proposed here are relatively cheap in the sense that computational effort is comparable to that required for tightening introduced by McEliece, Rodemich, Rumsey, and Schrijver.
Technical report TR-ISDS 2007-05, University of Vienna. To appear in: Mathematical Programming B (2012).