On the pebbling threshold of paths and the pebbling threshold spectrum

Andrzej Czygrinow, Glenn H. Hurlbert

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. A function is a pebbling threshold for a sequence of graphs if a randomly chosen configuration of asymptotically more pebbles is almost surely solvable, while one of asymptotically fewer pebbles is almost surely not. In this paper we tighten the gap between the upper and lower bounds for the pebbling threshold for the sequence of paths in the multiset model. We also find the pebbling threshold for the sequence of paths in the binomial model. Finally, we show that the spectrum of pebbling thresholds for graph sequences in the multiset model spans the entire range from n1 / 2 to n, answering a question of Czygrinow, Eaton, Hurlbert and Kayll. What the spectrum looks like above n remains unknown.

Original languageEnglish (US)
Pages (from-to)3297-3307
Number of pages11
JournalDiscrete Mathematics
Volume308
Issue number15
DOIs
StatePublished - Aug 6 2008

Fingerprint

Path
Multiset
Binomial Model
Configuration
Graph in graph theory
Vertex of a graph
Upper and Lower Bounds
Roots
Entire
Unknown
Model
Range of data
Statistical Models

Keywords

  • Paths
  • Pebbling
  • Spectrum
  • Threshold

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On the pebbling threshold of paths and the pebbling threshold spectrum. / Czygrinow, Andrzej; Hurlbert, Glenn H.

In: Discrete Mathematics, Vol. 308, No. 15, 06.08.2008, p. 3297-3307.

Research output: Contribution to journalArticle

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