Maximizing Several Cuts Simultaneously

Consider two graphs G1 and G2 on the same vertex set V and suppose that Gi has mi edges. Then there is a bipartition of V into two classes A and B so that for both i = 1, 2 we have eGi (A, B) ≥ mi/2 − √ mi. This gives an approximate answer to a question of Bollob´as and Scott. We also prove results about partitions into more than two vertex classes. Our proofs yield polynomial algorithms.

• Type: Journal
• Year: 2007
• Where: CPC
• Authors: Daniela Kühn, Deryk Osthus
• Keywords: Algorithms, Approximate Answer, CPC 2007, Polynomial