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\noindent
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{\bf Jonas Sj\"{o}strand}
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{\bf The Cover Pebbling Theorem}
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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 et cetera) 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.

\bye