Abstract
1The question of the connectivity is one of the funda� mental questions in the graph theory and it has a huge number of practical applications: integrated circuit design, reliable communication networks, planning of the transport networks, cluster analysis, and others. One of the basic combinatorial problems in this area is the problem of finding a minimum or a maximum cut in an undirected weighted graph. Instance 1. Given an undirected graph G = (V, E) and a function C: E → + that assigns a nonnegative integer number to every edge of the graph (that is called the weight of the edge). It is required to find such a partition of the vertex set V into two disjoint subsets P and Q (cut) that the sum of the edge weights of E, connecting the vertices of the sets P and Q, is as small as possible (minimum
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