Maximizing Several Cuts Simultaneously

Authors:
Daniela Kühn;Deryk Osthus
Affiliations:
School of Mathematics, Birmingham University, Edgbaston, Birmingham B15 2TT, UK (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk);School of Mathematics, Birmingham University, Edgbaston, Birmingham B15 2TT, UK (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
2007

Citing 4
Cited 1

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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 $e_{G_i}(A,B) \geq m_i/2-\sqrt{m_i}$. This gives an approximate answer to a question of Bollobás and Scott. We also prove results about partitions into more than two vertex classes. Our proofs yield polynomial algorithms.