Graphs and theory of stable allocation

The paper discusses a model of matching process which was proposed by two American mathematicians: David Gale and Lloyd S. Shapley. The basic concept defined by them was the stable allocation, which can be achieved with so-called deferred acceptance algorithm. The article analyzes the problems discussed by the theory of stable allocations on the basis of graph theory. It has been shown that the issues raised by this theory can be ana-lyzed using bipartite graphs and networks weighted. They also formulated conditions which should be met in purpose to solve a problem of matching. References relate to the labor market, as a discussed issue is applicable in practice, especially in the design of systems of recruitment companies. The aim of the article is to present the problem of bilateral associa-tions with the use of the language of graph theory and an indication of possible applications in the area of search and match of job seekers and employers