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Improved Pebbling Bounds

Melody Chan·Anant P. Godbole
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Abstract

Consider a configuration of pebbles distributed on the vertices of a connected graph of order $n$. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles on a graph is called solvable if it is possible to place a pebble on any given vertex using a sequence of pebbling steps. The pebbling number of a graph, denoted $f(G)$, is the minimal number of pebbles such that every configuration of $f(G)$ pebbles on $G$ is solvable. We derive several general upper bounds on the pebbling number, improving previous results.

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Melody Chan, Anant P. Godbole. 2005-10-03. Improved Pebbling Bounds. https://arxiv.org/abs/math/0510045

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