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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-19990 |
| Date | 28 January 2004 |
| Creators | Wierman, Adam, Salzman, Julia, Jablonski, Michael, Godbole, Anant P. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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