On the Pebbling Threshold Spectrum

Details On the Pebbling Threshold Spectrum On the Pebbling Threshold Spectrum

2004-06-07

arxiv.org/abs/math/0406124v1

Mathematics

Combinatorics

8 pages, preliminary version

Scientific paper

A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. A function is a pebbling threshold for a sequence of graphs if a randomly chosen configuration of asymptotically more pebbles is almost surely solvable, while one of asymptotically fewer pebbles is almost surely not. In this note we show that the spectrum of pebbling thresholds for graph sequences spans the entire range from n^{1/2} to n. This answers a question of Czygrinow, Eaton, Hurlbert and Kayll. What the spectrum looks like above n remains unknown.

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