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The Complexity of Graph Pebbling

K. Milans·B. Clark
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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 Π_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.

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K. Milans, B. Clark. 2005-03-30. The Complexity of Graph Pebbling. https://arxiv.org/abs/math/0503698

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