Document Type
Article
Publication Date
11-2009
Publication Title
European Journal of Combinatorics
Abstract
A hypergraph G=(V,E) is (k,ℓ)-sparse if no subset V′⊂V spans more than k|V′|−ℓ hyperedges. We characterize (k,ℓ)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address the problem of finding lower-dimensional representations of sparse hypergraphs, and identify a critical behavior in terms of the sparsity parameters k and ℓ. Our constructions extend the pebble games of Lee and Streinu [A. Lee, I. Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (8) (2008) 1425–1437] from graphs to hypergraphs.
Volume
30
Issue
8
First Page
1944
Last Page
1964
DOI
dx.doi.org/10.1016/j.ejc.2008.12.018
ISSN
0195-6698
Recommended Citation
Streinu, Ileana and Theran, Louis, "Sparse Hypergraphs and Pebble Game Algorithms" (2009). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/14
Comments
Author’s submitted manuscript.