Discrete Mathematics and Combinatorics Commons^™

Pebble Game Algorithms And Sparse Graphs, Audrey Lee, Ileana Streinu

Computer Science: Faculty Publications

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.