Cover Pebbling Hypercubes
Combinatorics
2007-05-23 v1
Abstract
Given a graph G and a configuration C of pebbles on the vertices of G, a pebbling step removes two pebbles from one vertex and places one pebble on an adjacent vertex. The cover pebbling number g=g(G) is the minimum number so that every configuration of g pebbles has the property that, after some sequence of pebbling steps, every vertex has a pebble on it. We prove that the cover pebbling number of the d-dimensional hypercube Q^d equals 3^d.
Cite
@article{arxiv.math/0409368,
title = {Cover Pebbling Hypercubes},
author = {Glenn H. Hurlbert and Benjamin Munyan},
journal= {arXiv preprint arXiv:math/0409368},
year = {2007}
}
Comments
11 pages