# Complexity of Max Bisection on cubic planar graphs?

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