On the pebbling threshold of paths and the pebbling threshold spectrum

Andrzej Czygrinow, Glenn H. Hurlbert

Research output: Contribution to journalArticle

2 Scopus citations

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

Keywords

  • Paths
  • Pebbling
  • Spectrum
  • Threshold

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'On the pebbling threshold of paths and the pebbling threshold spectrum'. Together they form a unique fingerprint.

  • Cite this