Explicit Unique-Neighbor Expanders

We present a simple, explicit construction of an infinite family F of bounded-degree 'unique-neighbor' expanders \Gamma; i.e., there are strictly positive constants \alpha and, such that all \Gamma = (X,E(\Gamma)) \varepsilon F satisfy the following property. For each subset S of X with no more than \alpha|X| vertices, there are at least \varepsilon|S| vertices in X \S that are adjacent in \Gamma to exactly one verte in S. The construction of F is simple to specify, and each \Gamma \varepsilon 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 several applications and settles an open problem considered by various researchers.