Bipartite subgraphs of integer weighted graphs

For every integer p > 0, let f(p) be the minimum possible value of the maximum weight of a cut in an integer weighted graph with total weight p. It is shown that for every large n and every m < n, f((n)(2)) + m) = right perpendicular 1/4n(2) left perpendicular + min(inverted right perpendicular 1/2n inverted left perpendicular. This supplies the precise value of f(p) for many values of p including, e.g., all p = ((n)(2)) + ((m)(2)) when n is large enough and 1/4m(2) less than or equal to 1/2n.