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arXiv · 1601.02229

Constructions for the optimal pebbling of grids

Ervin Győri·Gyula Y. Katona·László F. Papp
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Abstract

In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics] the authors conjecture that if every vertex of an infinite square grid is reachable from a pebble distribution, then the covering ratio of this distribution is at most $3.25$. First we present such a distribution with covering ratio $3.5$, disproving the conjecture. The authors in the above paper also claim to prove that the covering ratio of any pebble distribution is at most $6.75$. The proof contains some errors. We present a few interesting pebble distributions that this proof does not seem to cover and highlight some other difficulties of this topic.

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Ervin Győri, Gyula Y. Katona, László F. Papp. 2017-04-06. Constructions for the optimal pebbling of grids. https://doi.org/10.3311/ppee.9724

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