Abstract We studied the minimum cut cover problem that consists in finding a minimum cardinality family of cuts C of a graph G such that each edge of G belongs to at least one cut C ∈ C . This problem is NP -hard and arises in fault testing and diagnosis, pattern recognition, and biological identification. We propose here a new integer programming formulation and a new exact algorithm for the problem. We also proposed a simple heuristic and made empirical experiments to compare it with those reported in the literature. It is an ongoing work. The preliminary results show that the dual bounds provided by the new formulation are tighter than those obtained using the earlier one and the primal bounds given by our heuristic are near optimal for the small instances and tighter than other reported in the literature.