 
Summary: An Elementary Construction of ConstantDegree Expanders
Noga Alon
Oded Schwartz
Asaf Shapira
Abstract
We describe a short and easy to analyze construction of
constantdegree expanders. The construction relies on the
replacement product, applied by [14] to give an iterative
construction of boundeddegree expanders. Here we give a
simpler construction, which applies the replacement product
(only twice!) to turn the Cayley expanders of [4], whose
degree is polylog n, into constant degree expanders. This
enables us to prove the required expansion using a new
simple combinatorial analysis of the replacement product
(instead of the spectral analysis used in [14]).
1 Introduction
All graphs considered here are finite, undirected and
may contain selfloops and parallel edges. Expanders
are graphs, which are simultaneously sparse, yet highly
connected, in the sense that every cut contains (rel
