A new second–order cone programming relaxation for max-cut problems

We propose a new relaxation scheme for the MAX–CUT problem using second-order cone programming. We construct relaxation problems to reflect the structure of the original graph. Numerical experiments show that our relaxation gives better bounds than those based on the spectral decomposition proposed by Kim and Kojima, and that the efficiency of the branch-and-bound method using our relaxation is comparable to that using semidefinite relaxation in some cases.