On pebbling threshold functions for graph sequences
Date of Original Version
Given a connected graph G, and a distribution of / pebbles to the vertices of G, a pebbling step consists of removing two pebbles from a vertex v and placing one pebble on a neighbor of v. For a particular vertex r, the distribution is r-solvable if it is possible to place a pebble on r after a finite number of pebbling steps. The distribution is solvable if it is r-solvable for every r. The pebbling number of G is the least number /, so that every distribution of t pebbles is solvable. In this paper we are not concerned with such an absolute guarantee but rather an almost sure guarantee. A threshold function for a sequence of graphs 'S = (Gi,G2,...,G,...), where G has n vertices, is any function ta(n) such that almost all distributions of / pebbles are solvable when t>t0, and such that almost none are solvable when t<$to. We give bounds on pebbling threshold functions for the sequences of cliques, stars, wheels, cubes, cycles and paths. © 2002 Elsevier Science B.V. All rights reserved.
Publication Title, e.g., Journal
Czygrinow, Andrzej, Nancy Eaton, Glenn Huribert, and P. M. Kayll. "On pebbling threshold functions for graph sequences." Discrete Mathematics 247, 1-3 (2002): 93-105. doi: 10.1016/S0012-365X(01)00163-7.