Orthogonal [k-1,k+1]-factorizations in graphs

Let G be a graph. Let F = {F-1,F-2,...,F-d} be a factorization of G and H be a subgraph of G. If H has exactly one edge in common with F-i for all i = 1,2,...,d, then we say that F is orthogonal to H. In this paper it is proved that for any d-matching M of a [kd - 1, kd + 1]-graph G, there is a [k - 1, k + 1]-factorization of G orthogonal to M where k greater than or equal to 2 is an integer.