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A Survey of Graph Pebbling

Glenn Hurlbert
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Abstract

We survey results on the pebbling numbers of graphs as well as their historical connection with a number-theoretic question of Erd\H os and Lemke. We also present new results on two probabilistic pebbling considerations, first the random graph threshold for the property that the pebbling number of a graph equals its number of vertices, and second the pebbling threshold function for various natural graph sequences. Finally, we relate the question of the existence of pebbling thresholds to a strengthening of the normal property of posets, and show that the multiset lattice is not supernormal.

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Glenn Hurlbert. 2004-06-01. A Survey of Graph Pebbling. https://arxiv.org/abs/math/0406024

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