A note on optimal pebbling of hypercubes

Hung-Lin Fu (), Kuo-Ching Huang () and Chin-Lin Shiue ()
Additional contact information
Hung-Lin Fu: National Chiao Tung University
Kuo-Ching Huang: Providence University
Chin-Lin Shiue: Chung Yuan Christian University

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 9, 597-601

Abstract: Abstract A pebbling move consists of removing two pebbles from one vertex and then placing one pebble at an adjacent vertex. If a distribution δ of pebbles lets us move at least one pebble to each vertex by applying pebbling moves repeatedly(if necessary), then δ is called a pebbling of G. The optimal pebbling number f′(G) of G is the minimum number of pebbles used in a pebbling of G. In this paper, we improve the known upper bound for the optimal pebbling number of the hypercubes Q n . Mainly, we prove for large n, $f'(Q_{n})=O(n^{3/2}(\frac {4}{3})^{n})$ by a probabilistic argument.

Keywords: Optimal pebbling; Hypercubes (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-012-9492-9

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