Abstract. The paper considers the minimization of the sum of weights of edges forming a subset of the set of disjoint simple cycles at the vertices in the graph H = (V, U) and cover V. This problem (2-f problem) is solvable in polynomial algorithms, which are characterized by technical difficulties that hinder accelerate computing. The solution of 2-f is reducing it to a simple bipartite case. The desired result is represented by a perfect matching of a bipartite graph corresponding to the solution of the assignment problem, in which each expansion cycle circuit comprises at least three arcs.

Keywords: 2-factor, the assignment problem, matching, bipartite graph, increasing path.