On embedding expanders into lp spaces

In this note we show that the minimum distortion required to embed ail n-point metric spaces into the Banach space e(p) is between (c(1)/p) log n and (c(2)/p) log n, where c(2) > c(1) > 0 are absolute constants and 1 less than or equal to p < log n. The lower bound is obtained by a generalization of a method of Linial et al. [LLR95], by showing that constant-degree expanders (considered as metric spaces) cannot be embedded any better.