  In this note we answer a question of Hurlbert about pebbling in graphs of
high girth. Specifically we show that for every g there is a Class 0 graph of
girth at least g. The proof uses the so-called Erdos construction and employs a
recent result proved by Czygrinow, Hurlbert, Kierstead and Trotter. We also use
the Czygrinow et al. result to prove that Graham's pebbling product conjecture
holds for dense graphs. Finally, we consider a generalization of Graham's
conjecture to thresholds of graph sequences and find reasonably tight bounds on
the pebbling threshold of the sequence of d-dimensional grids, verifying an
important instance the generalization.
