Packing of graphic n-tuples

An n-tuple p (not necessarily monotone) is graphic if there is a simple graph G with vertex set {v1, ..., vn} in which the degree of vi is the ith entry of p. Graphic n-tuples (d?(1)1,..., d?(1)n) and (d?(2)1,..., d?(2)n) pack if there are edge-disjoint n-vertex graphs G1 and G2 such that d?G?1(vi) = d?(1)i and d?G?2(vi) = d?(2)i for all i. We prove that graphic n-tuples p1 and p2 pack if , where ?and ddenote the largest and smallest entries in p1 + p2 (strict inequality when d = 1); also, the bound is sharp.