Abstract : This paper contains the following results. For a sequence A, let (M sub A) be the number of non-zero entries in it; suppose A, B and C = (A+B) are sequences that are the degrees of simple graphs; then if summation of (c sub i) or or = 2(M sub A) + (M sub B) - 2, there exists a realization of C having disjoint factors with degree sequences A and B. At least one of these can be a forest. If A and B are forest realizable, the conditions under which A, B and C can be simultaneously realized with A- and B-factors that are forests are characterized.