Mathematical Programming

, Volume 124, Issue 1, pp 13–32

Copositivity cuts for improving SDP bounds on the clique number

  • Immanuel M. Bomze
  • Florian Frommlet
  • Marco Locatelli
Full Length Paper Series B

DOI: 10.1007/s10107-010-0363-9

Cite this article as:
Bomze, I.M., Frommlet, F. & Locatelli, M. Math. Program. (2010) 124: 13. doi:10.1007/s10107-010-0363-9


Adding cuts based on copositive matrices, we propose to improve Lovász’ bound θ on the clique number and its tightening θ′ 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 starting with θ′ 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 θ′.


Lovász’ boundSemidefinite programmingMaximum clique problem

Mathematics Subject Classification (2000)


Copyright information

© Springer and Mathematical Programming Society 2010

Authors and Affiliations

  • Immanuel M. Bomze
    • 1
  • Florian Frommlet
    • 1
  • Marco Locatelli
    • 2
  1. 1.ISDS, University of ViennaViennaAustria
  2. 2.DII, University of ParmaParmaItaly