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) = n2 4 + min( n 2 , f(m)). 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 m2 4 ≤ n 2 .

• Type: Journal
• Year: 1998
• Where: DM
• Authors: Noga Alon, Eran Halperin
• Keywords: DM 1998, Integer, Maximum Weight, Minimum Possible Value