The Complexity of Graph Pebbling
arXiv:math/0503698
Abstract
We explore the complexity of computing the optimal pebbling number and pebbling number of a graph. We show that deciding whether the optimal pebbling number of G is at most k is NP-complete and deciding whether the pebbling number of G is at most k is Î _2-complete. Additionally, we provide a characterization of when an unordered set of pebbling moves can be ordered to form a valid sequence of pebbling moves.
24 pages, 6 figures