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

Airat Bekmetjev, Graham Brightwell, Andrzej Czygrinow, Glenn Hurlbert

Research output: Contribution to journalArticle

15 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)21-34
Number of pages14
JournalDiscrete Mathematics
Volume269
Issue number1-3
DOIs
StatePublished - Jul 28 2003

Keywords

  • Multiset lattice
  • Pebbling number
  • Shadow
  • Threshold

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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