Hypergraph expanders of all uniformities from Cayley graphs

TL;DR

This paper presents a generalized, simple construction method for hypergraph expanders of all uniformities, extending previous work on 3-uniform hypergraph expanders with polylogarithmic degree.

Contribution

It introduces a universal construction technique for hypergraph expanders across all uniformities, broadening the scope of previous specific cases.

Findings

Constructed hypergraph expanders for all uniformities r ≥ 3

Achieved hypergraph expanders with polylogarithmic degree

Simplified the construction process for hypergraph expanders

Abstract

Hypergraph expanders are hypergraphs with surprising, non-intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of $3$-uniform hypergraph expanders with polylogarithmic degree. We generalize this construction, giving a simple construction of $r$-uniform hypergraph expanders for all $r \geq 3$.