 
Summary: EXPLICIT UNIQUENEIGHBOR EXPANDERS
Extended Abstract
Noga Alon
Michael Capalbo
Abstract
We present a simple, explicit construction of an in
finite family F of boundeddegree 'uniqueneighbor' ex
panders ; i.e., there are strictly positive constants
and , such that all = (X, E()) F satisfy the
following property. For each subset S of X with no
more than X vertices, there are at least S vertices
in X \ S that are adjacent in to exactly one vertex
in S. The construction of F is simple to specify, and
each F is 6regular. We then extend the technique
and present easy to describe explicit infinite families
of 4regular and 3regular uniqueneighbor expanders,
as well as explicit families of bipartite graphs with non
equal color classes and similar properties. This has sev
eral applications and settles an open problem considered
by various researchers.
