Lower bounds for testing digraph connectivity with one-pass streaming   algorithms
  In this note, we show that three graph properties - strong connectivity, acyclicity, and reachability from a vertex $s$ to all vertices - each require a working memory of $\Omega (\epsilon m)$ on a graph with $m$ edges to be determined correctly with probability greater than $(1+\epsilon)/2$. 
Glencora Borradaile and Claire Mathieu and Theresa Migler
cs.DS cs.CC