A Survey of Graph Pebbling
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0406024,
title = {A Survey of Graph Pebbling},
author = {Glenn Hurlbert},
journal= {arXiv preprint arXiv:math/0406024},
year = {2007}
}
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24 pages