Optimization and optimality test for the Max-Cut Problem

We show that the following two problems are polynomiaUy equivalent: 1) Given a (weighted) graph G, and a cut C of G, decide whether C is maximal or not . 2) Given a (weighted) graph G, and a cut C of G, decide whether C is maximal or not , and in case it is not , find a better solution C'. As a consequence, an optimali ty testing oracle may be used to design a polynomial t ime algori thm for approximate ly solving the (weighted) Max-Cut Problem. This in turn implies that recognizing opt imal cuts in an unweighted graph is NP-hard.