The Pebbling Threshold of the Square of Cliques

Details The Pebbling Threshold of the Square of Cliques The Pebbling Threshold of the Square of Cliques

2004-06-08

arxiv.org/abs/math/0406157v1

Mathematics

Combinatorics

22 pages. Submitted to Discrete Mathematics

Scientific paper

Given an initial configuration of pebbles on a graph, one can move pebbles in pairs along edges, at the cost of one of the pebbles moved, with the objective of reaching a specified target vertex. The pebbling number of a graph is the minimum number of pebbles so that every configuration of that many pebbles can reach any chosen target. The pebbling threshold of a sequence of graphs is roughly the number of pebbles so that almost every (resp. almost no) configuration of asymptotically more (resp. fewer) pebbles can reach any chosen target. In this paper we find the pebbling threshold of the sequence of squares of cliques, improving upon an earlier result of Boyle and verifying an important instance of a probabilistic version of Graham's product conjecture.

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