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Max Bisection problem is to partition the set of nodes into two equal size sets such that the number of crossing edges is maximum. Max Bisection is $NP$-complete on cubic graphs and also on planar graphs.

What is the complexity of Max Bisection on cubic planar graphs? Is it $NP$-complete?

Cross posted on mathOverflow

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By "crossing edges" do you mean the edges whose endpoints are in both sets making up the bisection? – Joseph Malkevitch Jan 15 '11 at 4:01
    
Max Bisection is MAX CUT with additional requirement that the two node sets have the same cardinality. – Mohammad Al-Turkistany Jan 15 '11 at 8:23

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