Abstract
This paper contains the following results. For a sequence A, let $M_A $ be the number of nonzero entries in it; suppose $A,B$ and $C = ( {A + B} )$ are sequences that are the degrees of simple graphs; then if $\sum {c_i \geqq 2( {M_A + M_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.
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