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An Elementary Construction of Constant-Degree Expanders Oded Schwartz

Summary: An Elementary Construction of Constant-Degree Expanders
Noga Alon
Oded Schwartz
Asaf Shapira
We describe a short and easy to analyze construction of
constant-degree expanders. The construction relies on the
replacement product, applied by [14] to give an iterative
construction of bounded-degree 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 self-loops and parallel edges. Expanders
are graphs, which are simultaneously sparse, yet highly
connected, in the sense that every cut contains (rel-


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics