Constructions for the Optimal Pebbling of Grids

Authors

  • Ervin Győri
    Affiliation
    Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gyula Y. Katona
    Affiliation
    Department of Computer Science and Information Theory, Faculty of Electrical Engineering and Informatics, Budapest University of Technology and Economics, Hungary
  • László F. Papp
    Affiliation
    Department of Computer Science andInformation Theory, Faculty of Electrical Engineering and Informatics, Budapest University of Technology and Economics, Hungary
https://doi.org/10.3311/PPee.9724

Abstract

In [6] 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.

Keywords:

optimal pebbling, pebbling, grid graph

Citation data from Crossref and Scopus

Published Online

2017-05-23

How to Cite

Győri, E., Katona, G. Y., Papp, L. F. “Constructions for the Optimal Pebbling of Grids”, Periodica Polytechnica Electrical Engineering and Computer Science, 61(2), pp. 217–223, 2017. https://doi.org/10.3311/PPee.9724

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Articles