Some results on orthogonal factorizations

Consider a graph G = (V,E) with an [a, b]-factorization F = {F-1, F-2,..., F-m}. It is proved in this paper that: 1. there is an m-matching of G to which F is orthogonal if n = \V(G)\ greater than or equal to (2 + b/a)(m - 1) for b greater than or equal to 2a and n greater than or equal to 3.26m for b = a; 2. if root2b less than or equal to a less than or equal to b, then for any given edge e of G, there is a [1, a]-subgraph H of G such that e is included in H and F is orthogonal to H.