The paper [11] raised the question of describing cardinality and types approximations for natural families theories. In present paper, a partial answer to this is given, study approximation topological properties classes theories also continued. We consider cycle graph consisting one or, in other words, certain number vertices (at least 3 if simple) connected into closed chain. It shown that an...

A 1-factorisation of a graph G is a partition of the edge set of G into 1factors (perfect matchings); a perfect 1-factorisation of G is a 1-factorisation of G in which the union of any two of the 1-factors is a Hamilton cycle in G. It is known that for bipartite 4-regular circulant graphs, having order 2 (mod 4) is a necessary (but not sufficient) condition for the existence of a perfect 1-fact...