3-Monotone Expanders

Expanders are classes of highly connected graphs that are of fundamental importance in graph theory, with numerous applications, especially in theoretical computer science [29]. While the literature contains various definitions of expanders, this paper focuses on bipartite expanders. For ∈ (0, 1], a bipartite graph G with bipartition V (G) = A ∪ B is a bipartite -expander if |A| = |B| and |N(S)| > (1 + )|S| for every subset S ⊂ A with |S| 6 |A| 2 . Here N(S) is the set of vertices adjacent to some vertex in S. An infinite family of bipartite -expanders, for some fixed > 0, is called an infinite family of bipartite expanders.