Explicit unique-neighbor expanders

We present a simple, explicit construction of an infinite family F of bounded-degree ´unique-neighbor´ expanders Γ; i.e., there are strictly positive constants α and ε, such that all Γ = (X, E(Γ)) ∈ F satisfy the following property. For each subset S of X with no more than α|X| vertices, there are at least ε|S| vertices in X/S that are adjacent in Γ to exactly one vertex in S. The construction of F is simple to specify, and each Γ ∈ 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 nonequal color classes and similar properties. This has several applications and settles an open problem considered by various researchers.