and

We extend the notion of a potentially H-graphic sequence as fol-lows. Let A and B be nonnegative integer sequences. The sequence pair S = (A; B) is said to be bigraphic if there is some bipartite graph G = (X [Y; E) such that A and B are the degrees of the vertices in X and Y, respectively. If S is a bigraphic pair, let (S) denote the sum of the terms in A. Given a bigraphic pair S, and a xed bipartite graph H, we say that S is potentially H-bigraphic if there is some realization of S containing H as a subgraph. We dene (H; m; n) to be the minimum integer k such that every bigraphic pair S = (A; B) with jAj = m; jBj = n and (S) k is potentially H-bigraphic. In this paper, we determin