Thresholds for families of multisets, with an application to graph pebbling

Authors:
Airat Bekmetjev;Graham Brightwell;Andrzej Czygrinow;Glenn Hurlbert
Affiliations:
Department of Mathematics, Arizona State University, Tempe, AZ;Department of Mathematics, London School of Economics, London, WC2A 2AE, UK;Department of Mathematics, Arizona State University, Tempe, AZ;Department of Mathematics, Arizona State University, Tempe, AZ
Venue:
Discrete Mathematics
Year:
2003

Citing 2
Cited 3

Threshold functions

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On pebbling threshold functions for graph sequences

Discrete Mathematics

On pebbling threshold functions for graph sequences

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Thresholds for random distributions on graph sequences with applications to pebbling

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General graph pebbling

Discrete Applied Mathematics

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Abstract

In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász's version of the Kruskal-Katona Theorem and an analog of the Bollobás-Thomason threshold result. As a corollary we obtain the existence of pebbling thresholds for arbitrary graph sequences. In addition, we improve both the lower and upper bounds for the 'random pebbling' threshold of the sequence of paths.