On pebbling threshold functions for graph sequences

Andrzej Czygrinow, Nancy Eaton, Glenn Huribert, P. Mark Kayll

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Given a connected graph G, and a distribution of / pebbles to the vertices of G, a pebbling step consists of removing two pebbles from a vertex v and placing one pebble on a neighbor of v. For a particular vertex r, the distribution is r-solvable if it is possible to place a pebble on r after a finite number of pebbling steps. The distribution is solvable if it is r-solvable for every r. The pebbling number of G is the least number /, so that every distribution of t pebbles is solvable. In this paper we are not concerned with such an absolute guarantee but rather an almost sure guarantee. A threshold function for a sequence of graphs 'S = (Gi,G2,...,G,...), where G has n vertices, is any function ta(n) such that almost all distributions of / pebbles are solvable when t>t0, and such that almost none are solvable when t<$to. We give bounds on pebbling threshold functions for the sequences of cliques, stars, wheels, cubes, cycles and paths.

Original languageEnglish (US)
Pages (from-to)93-105
Number of pages13
JournalDiscrete Mathematics
Volume247
Issue number1-3
StatePublished - Mar 28 2002

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Threshold Function
Graph in graph theory
Stars
Wheels
Vertex of a graph
Clique
Wheel
Regular hexahedron
Connected graph
Star
Cycle
Path

Keywords

  • Pebbling number
  • S0012-365X(01)00163-7
  • Threshold function

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Czygrinow, A., Eaton, N., Huribert, G., & Kayll, P. M. (2002). On pebbling threshold functions for graph sequences. Discrete Mathematics, 247(1-3), 93-105.

On pebbling threshold functions for graph sequences. / Czygrinow, Andrzej; Eaton, Nancy; Huribert, Glenn; Kayll, P. Mark.

In: Discrete Mathematics, Vol. 247, No. 1-3, 28.03.2002, p. 93-105.

Research output: Contribution to journalArticle

Czygrinow, A, Eaton, N, Huribert, G & Kayll, PM 2002, 'On pebbling threshold functions for graph sequences', Discrete Mathematics, vol. 247, no. 1-3, pp. 93-105.
Czygrinow A, Eaton N, Huribert G, Kayll PM. On pebbling threshold functions for graph sequences. Discrete Mathematics. 2002 Mar 28;247(1-3):93-105.
Czygrinow, Andrzej ; Eaton, Nancy ; Huribert, Glenn ; Kayll, P. Mark. / On pebbling threshold functions for graph sequences. In: Discrete Mathematics. 2002 ; Vol. 247, No. 1-3. pp. 93-105.
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