Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 $i=1,2$,  have $e_{G_i}(A,B) \geq m_i/2-\sqrt{m_i}$. This gives an approximate ansr to a question of Bollobas and Scott.  also prove results about partitions into more than two vertex classes. Our proofs yield polynomial algorithms.
['Daniela Kühn', 'Deryk Osthus']
I am writing a research paper on a idea Maximizing Several Cuts Simultaneously
[{"from": "human", "value": "I am writing a research paper on a idea Maximizing Several Cuts Simultaneously"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 $i=1,2$,  have $e_{G_i}(A,B) \\geq m_i/2-\\sqrt{m_i}$. This gives an approximate ansr to a question of Bollobas and Scott.  also prove results about partitions into more than two vertex classes. Our proofs yield polynomial algorithms."}]