  For any configuration of pebbles on the nodes of a graph, a pebbling move
replaces two pebbles on one node by one pebble on an adjacent node. A cover
pebbling is a move sequence ending with no empty nodes. The number of pebbles
needed for a cover pebbling starting with all pebbles on one node is trivial to
compute and it was conjectured that the maximum of these simple cover pebbling
numbers is indeed the general cover pebbling number of the graph. That is, for
any configuration of this size, there exists a cover pebbling. In this note, we
prove a generalization of the conjecture. All previously published results
about cover pebbling numbers for special graphs (trees, hypercubes etcetera)
are direct consequences of this theorem. We also prove that the cover pebbling
number of a product of two graphs equals the product of the cover pebbling
numbers of the graphs.
