Pebble game algorithms and sparse graphs

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 values k and ℓ ∈ [0, 2 k), we characterize the (k, ℓ)-sparse graphs via a family of simple, elegant and efficient algorithms called the (k, ℓ)-pebble games. © 2007 Elsevier B.V. All rights reserved.