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

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

2004-06-03

arxiv.org/abs/math/0406068v1

Discrete Math. 269 (2003), no.1-3, 21--34

Mathematics

Combinatorics

17 pages

Scientific paper

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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