Orthogonal (g,f)-factorizations in graphs Original Research Article

Let G be a graph and let F = F1, F2, …, Fm and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with Fi for all i, 1 ⩽ i ⩽ 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) ⩽ f(x) for every x ϵ V(G). In this paper it is proved that for any m-matchingM of an (mg + m − 1, mf − m + 1)-graph G, there exists a (g,f)-factorization of G orthogonal to M.