# Expanders, Property Testing and the PCP theorem

## Student Presentation # 9

Posted in presentations by atri on January 13, 2009

(Guest post by Steve Uurtamo)

I presented the result (by Noga Alon, Eldar Fischer, Ilan Newman and Asaf Shapira) that using the dense graph model and allowing for two-sided error, the set of graph properties that can be tested for using a constant number of queries to the adjacency matrix of a graph (constant for any fixed error distance $\epsilon$) exactly correspond with those that can be determined using a set of Szemeredi regularity constraints.

Three examples of such reductions are given in the paper; vertex $k$-colorability (testable), co-subgraph isomorphism (testable) and graph isomorphism (not testable).