ORTHOGONAL (G,F)-FACTORIZATIONS IN GRAPHS

Let G be a graph and let F = {F-1, F-2,..., F-m} and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with F-i for all i, 1 less than or equal to i less than or equal to m, then we say that F is orthogonal to H. Let g and f be two integer-valued functions defined on V(G) such that g(x) less than or equal to f(x) for every x is an element of V(G). In this paper it is proved that for any m-matching M of an (mg + m - 1, mf - m + 1)-graph G, there exists a (g, f)-factorization of G orthogonal to M.