Bipartite subgraphs of integer weighted graphs

Noga Alon*, Eran Halperin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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((n2) + m) = ⌊1/4n2⌋ + min(⌈1/2n⌉, f(m)). This supplies the precise value of f(p) for many values of p including, e.g., all p = (n2) + (m2) when n is large enough and 1/4m2 ≤ 1/2n.

Original languageEnglish
Pages (from-to)19-29
Number of pages11
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 15 Feb 1998


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