Pebble Game Algorithms and Sparse Graphs

Authors

Audrey Lee, University of Massachusetts Amherst
Ileana Streinu, Smith CollegeFollow

Document Type

Article

Publication Date

4-28-2008

Abstract

A multi-graph G on n vertices is (k,ℓ)-sparse if every subset of n^′⩽n vertices spans at most kn^′-ℓ edges. G is tight if, in addition, it has exactly kn-ℓ edges. For integer valuesk and ℓ∈[0,2k), we characterize the (k,ℓ)-sparse graphs via a family of simple, elegant and efficient algorithms called the (k,ℓ)-pebble games. [A. Lee, I. Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (8) (2008) 1425–1437] from graphs to hypergraphs.

Keywords

Sparse graph, Pebble game, Henneberg sequence, Matroid, Circuit, Rigidity

Volume

308

Issue

8

First Page

1425

Last Page

1437

DOI

dx.doi.org/10.1016/j.disc.2007.07.104/

ISSN

0012-365X

Comments

Author’s submitted manuscript.

Recommended Citation

Lee, Audrey and Streinu, Ileana, "Pebble Game Algorithms and Sparse Graphs" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/16