Finite graphs and amenability

Elek, Gábor (2012) Finite graphs and amenability. Journal of Functional Analysis, 263 (9). pp. 2593-2614. ISSN 0022-1236

Abstract

Hyperfiniteness or amenability of measurable equivalence relations and group actions has been studied for almost fifty years. Recently, unexpected applications of hyperfiniteness were found in computer science in the context of testability of graph properties. In this paper we propose a unified approach to hyperfiniteness. We establish some new results and give new proofs of theorems of Schramm, Lovász, Newman–Sohler and Ornstein–Weiss.