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

The degree-constrained subgraphs decomposition problem, such as an f-coloring, an f-factorization, and a [ g, f ]-factorization, is to decompose a given graph G=(V, E) to edge-disjoint subgraphs degree-constrained by integer-valued functions f and g on V. 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 integer k, we give a polynomial-time transformation of G to a new graph such that G can be decomposed to at most k degree-constrained subgraphs if and only if the new graph can be edge-colored with k colors. 1999 Academic Press