  Consider a configuration of pebbles distributed on the vertices of a
connected graph of order $n$. A pebbling step consists of removing two pebbles
from a given vertex and placing one pebble on an adjacent vertex. A
distribution of pebbles on a graph is called solvable if it is possible to
place a pebble on any given vertex using a sequence of pebbling steps. The
pebbling number of a graph, denoted $f(G)$, is the minimal number of pebbles
such that every configuration of $f(G)$ pebbles on $G$ is solvable. We derive
several general upper bounds on the pebbling number, improving previous
results.
