Elsevier

Discrete Mathematics

Volume 308, Issue 8, 28 April 2008, Pages 1425-1437
Discrete Mathematics

Pebble game algorithms and sparse graphs

https://doi.org/10.1016/j.disc.2007.07.104Get rights and content
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Abstract

A multi-graph G on n vertices is (k,)-sparse if every subset of nn vertices spans at most kn- edges. G is tight if, in addition, it has exactly kn- edges. For integer values k and [0,2k), we characterize the (k,)-sparse graphs via a family of simple, elegant and efficient algorithms called the (k,)-pebble games.

Keywords

Sparse graph
Pebble game
Henneberg sequence
Matroid
Circuit
Rigidity

Cited by (0)

1

Research supported by an NSF graduate research fellowship and by the NSF Grant CCR-0310661 of the second author.

2

Research partially funded by NSF Grant CCR-0310661.