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

Airat Bekmetjev·Graham Brightwell·Andrzej Czygrinow·Glenn Hurlbert
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Abstract

In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovasz's version of the Kruskal-Katona Theorem and an analog of the Bollobas-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.

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Airat Bekmetjev, Graham Brightwell, Andrzej Czygrinow, Glenn Hurlbert. 2004-06-03. Thresholds for families of multisets, with an application to graph pebbling. https://arxiv.org/abs/math/0406068

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