A note on graph pebbling

Andrzej Czygrinow, Glenn Hurlbert, Henry Kierstead, William T. Trotter

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let k(d) denote the least positive integer so that every graph G with diameter at most d and connectivity at least k(d) is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must satisfy k(d) = 0(2d/d). In this note, we show that k exists and satisfies k(d) = O(22d). We also apply this result to improve the upper bound on the random graph threshold of the Class 0 property.

Original languageEnglish (US)
Pages (from-to)219-225
Number of pages7
JournalGraphs and Combinatorics
Volume18
Issue number2
DOIs
StatePublished - Dec 1 2002

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Keywords

  • Connectivity
  • Pebbling
  • Threshold

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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