Power estimation of the full set of alternatives to Paret's subgraphs in a graph

In practice problems of creation of an optimum subgraph of a certain look in a given graph count often meet. As possible annexes problems of search of optimum structure of technological networks, design of architecture of computers, modeling of artificial intelligence and many others are used. More and more relevant are multicriteria options of the specified tasks. An essential limiting factor of improvement of methods of multicriteria optimization on graphs is the problem of their exponential computing complexity caused by big dimension of a task. A number of data demonstrates that the theoretical assessment of complexity constructed for methods of full search isn't true, and the drawn conclusions have no sufficient justification. Among effective decisions the so-called complete set of alternatives which power can be lower on orders, than the power of the Pareto set is of the greatest interest. Taking into account the listed facts in this work the result of researches consisting in creation of assessment from above for the power of a complete set of alternatives of a problem of stay is stated pareto-optimal subgraphs for a given graph.