A generalized “wave” method for solving extremal problems on graphs

An optimization complex of a graph is constructed, and on the basis of this a statement is formalized in the class of wave subgraphs introduced in this paper also, and a solution of extremal problems on an arbitrary flow graph is given. The applicability of the method to the solution of multi-iteration problems is considered using the example of the problem of the greatest pair-combination of a bipartite graph. A new algorithm with an estimate of complexity improving the known estimate $O(n^{5/2})$ is presented.