A note on optimal pebbling of hypercubes

Abstract

A pebbling move consists of removing two pebbles from one vertex and then placing one pebble at an adjacent vertex. If a distribution delta of pebbles lets us move at least one pebble to each vertex by applying pebbling moves repeatedly(if necessary), then delta 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, by a probabilistic argument.