Applying the Branch-and-Bound method to solve the problem of hyper-graph dichotomous division

Application of the method of branches and bounds in order to solve the problem of hyper-graph dichotomous division by the criterion of minimum quantity of edges inside the section, is considered. New mathematical model guaranteeing a possibility to construct the decision treble, is proposed. It is proved that the minimum of the number of edges between the hyper-graph parts, meets requirements to the lower limit of the objective function. Concepts to realise the branch and boundary method are chosen; an approach to form the division alternatives is developed. The problems to encode the decision treble nodes are considered.