Decompositions to Degree-Constrainded Subgraphs Are Simply Reducible to Edge-Colorings

The degree-constrained subgraphs decomposition problem, such as anf-coloring, anf-factorization, and a [g,f]-factorization, is to decompose a given graphG=(V,E) to edge-disjoint subgraphs degree-constrained by integer-valued functionsfandgonV. In this paper we show that the problem can be simply reduced to the edge-coloring problem in polynomial-time. That is, for any positive integerk, we give a polynomial-time transformation ofGto a new graph such thatGcan be decomposed to at mostkdegree-constrained subgraphs if and only if the new graph can be edge-colored withkcolors.