(This is a revised version of work that was posted on arXiv in July 2010.)

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq3$ and tree-minors in bounded-degree graphs.
The complexity of these algorithms is related to the distance
of the graph from being ... more >>>

We study property testing in the model of bounded degree graphs. It
is well known that in this model many graph properties cannot be
tested with a constant number of queries and it seems reasonable to
conjecture that only few are testable with o(sqrt{n}) queries.
Therefore in this paper ... more >>>