Abstract
Consider two graphs G(1) and G(2) on the same vertex set V and suppose that G(i) has m(i) edges. Then there is a bipartition of V into two classes A and B so that, for both i = 1, 2, we have eG(i) (A, B) >= m(i)/2 - root(m(i)) over bar. This gives an approximate answer to a question of Bollobas and Scott. We also prove results about partitions into more than two vertex classes. Our proofs yield polynomial algorithms.
Original language | English |
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Pages (from-to) | 277-283 |
Number of pages | 7 |
Journal | Combinatorics, Probability and Computing |
Volume | 16 |
Issue number | 02 |
Early online date | 14 Aug 2006 |
DOIs | |
Publication status | Published - 1 Mar 2007 |