Geodesic
The cover pebbling theorem
The electronic journal of combinatorics, Tome 12 (2005)
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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.
DOI : 10.37236/1989
Classification : 05C35, 91A43
Mots-clés : Pebbling cover, Weighted pebbling cover 
@article{10_37236_1989,
     author = {Jonas Sj\"ostrand},
     title = {The cover pebbling theorem},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1989},
     zbl = {1081.05048},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1989/}
}
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Jonas Sjöstrand. The cover pebbling theorem. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1989

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