The union of matroids and the rigidity of frameworks
SIAM Journal on Discrete Mathematics
The molecule problem: determining conformation from pairwise distances
The molecule problem: determining conformation from pairwise distances
A matroid approach to finding edge connectivity and packing arborescences
Selected papers of the 23rd annual ACM symposium on Theory of computing
An algorithm for two-dimensional rigidity percolation: the pebble game
Journal of Computational Physics
On decomposing a hypergraph into k connected sub-hypergraphs
Discrete Applied Mathematics - Submodularity
Analyzing rigidity with pebble games
Proceedings of the twenty-fourth annual symposium on Computational geometry
Body-and-cad geometric constraint systems
Proceedings of the 2009 ACM symposium on Applied Computing
Body-and-cad geometric constraint systems
Computational Geometry: Theory and Applications
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A hypergraph G=(V,E) is (k,@?)-sparse if no subset V^'@?V spans more than k|V^'|-@? hyperedges. We characterize (k,@?)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovasz, 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 @?. 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.