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# Testing Expansion in Bounded Degree Graphs

Report ID:
TR-789-07
Authors:
Date:
June 2007
Pages:
7
Download Formats:
[PDF]

#### Abstract:

We consider the problem of testing graph expansion in the bounded degree model. We give a property tester that given a graph with degree bound $d$, an
expansion bound $\alpha$, and a parameter $\epsilon > 0$, accepts the graph with high probability if its expansion is more than $\alpha$, and rejects it with high probability if it is $\epsilon$-far from a graph with expansion $\Omega(\alpha2)$. The algorithm runs in time $\tilde{O}(\frac{n^{0.5 + \mu}d2}{\epsilon\alpha2})$ for any given constant $\mu > 0$.

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