An Expansion Tester for Bounded Degree Graphs

We consider the problem of testing graph expansion (either vertex or edge) in the bounded degree model [O. Goldreich and D. Ron, On Testing Expansion in Bounded-Degree Graphs, Technical report TR00-020, ECCC, Potsdam, Germany, 2000]. We give a property tester that takes as input a graph with degree bound $d$, an expansion bound $\alpha$, and a parameter $\varepsilon>0$. The tester accepts the graph with high probability if its expansion is more than $\alpha$, and rejects it with high probability if it is $\varepsilon$-far from any graph with expansion $\alpha'$ with degree bound $d$, where $\alpha' 0$.