Abstract: The Reeb graph R(f) of a C^1-function f from M to the real numbers with isolated critical points is a quotient object by the identification of connected components of function levels which has a natural structure of graph. The quotient map p from M to R(f) induces a homomorphism p* from the fundamental group of M to the fundamental group of R(f) which is equal to F_r, the free group of r generators. This leads to the natural question whether every epimorphism from a finitely presented group G to F_r can be represented as the Reeb epimorphism p* for a suitable Reeb (or even Morse) function f. We present a positive answer to this question. This is done by use of a construction of correspondence between epimorphisms from the fundamental group of M to F_r and systems of r framed non-separating hypersurfaces in M, which induces a bijection onto their framed cobordism classes. As applications we provide new purely geometrical-topological proofs of some algebraic facts.