An Improved Upper Bound for the Pebbling Threshold of the n-path
Document Type
Article
Publication Date
1-28-2004
Description
Given a configuration of t indistinguishable pebbles on the n vertices of a graph G, we say that a vertex v can be reached if a pebble can be placed on it in a finite number of "moves". G is said to be pebbleable if all its vertices can be thus reached. Now given the n-path Pn how large (resp. small) must t be so as to be able to pebble the path almost surely (resp. almost never)? It was known that the threshold th(Pn) for pebbling the path satisfies n2clgn≤th(Pn)≤n22lgn, where lg=log2 and c<1/2 is arbitrary. We improve the upper bound for the threshold function to th(Pn)≤n2dlgn, where d>1 is arbitrary.
Citation Information
Wierman, Adam; Salzman, Julia; Jablonski, Michael; and Godbole, Anant P.. 2004. An Improved Upper Bound for the Pebbling Threshold of the n-path. Discrete Mathematics. Vol.275(1-3). 367-373. https://doi.org/10.1016/j.disc.2002.10.001 ISSN: 0012-365X