Continuing from the previous post, we are going to prove the following result: let be a -regular Cayley graph of an Abelian group, be the normalized edge expansion of , be the value of the ARV semidefinite programming relaxation of sparsest cut on (we will define it below), and be the second smallest normalized Laplacian eigenvalue of . Then we have

which, together with the fact that and , implies the Buser inequality

The proof of (1), due to Shayan Oveis Gharan and myself, is very similar to the proof by Bauer et al. of (2).