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EXPLICIT UNIQUE-NEIGHBOR EXPANDERS Extended Abstract
 

Summary: EXPLICIT UNIQUE-NEIGHBOR EXPANDERS
Extended Abstract
Noga Alon
Michael Capalbo
Abstract
We present a simple, explicit construction of an in-
finite family F of bounded-degree 'unique-neighbor' 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 6-regular. We then extend the technique
and present easy to describe explicit infinite families
of 4-regular and 3-regular unique-neighbor 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.

  

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

 

Collections: Mathematics