Before revision:  In particular , our result provide a polynomial time O(\sqrt{\log \gamma})-approximation to the sparsest cut problem on planar graph , for the case where all the demand pairs can be covered by \gamma faces.
After revision:  In particular , our result provide a polynomial time O(\sqrt{\log \gamma})-approximation to the sparsest cut problem on planar graphs , for the case where all the demand pairs can be covered by \gamma faces.