 
Summary: Testing of bipartite graph properties
Noga Alon
Eldar Fischer
Ilan Newman§
June 15, 2005
Abstract
Alon et. al. [3], showed that every property that is characterized by a finite collection of
forbidden induced subgraphs is testable. However, the complexity of the test is doubletower
with respect to 1/ , as the only tool known to construct such tests is via a variant of Szemer´edi's
Regularity Lemma. Here we show that any property of bipartite graphs that is characterized by
a finite collection of forbidden induced subgraphs is testable, with a number of queries that is
polynomial in 1/ .
Our main tool is a new `conditional' version of the regularity lemma for binary matrices,
which may be interesting on its own.
A preliminary (and weaker) version of these results formed part of [9].
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel
Aviv University, Tel Aviv, Israel, and IAS, Princeton, NJ 08540, USA. Email: nogaa@tau.ac.il Research supported
in part by a grant from the Israel Science Foundation, by the Hermann Minkowski Minerva Center for Geometry at
