Sparse hypergraphs and pebble game algorithms

@article{Streinu2009SparseHA,
  title={Sparse hypergraphs and pebble game algorithms},
  author={Ileana Streinu and Louis Theran},
  journal={Eur. J. Comb.},
  year={2009},
  volume={30},
  pages={1944-1964}
}
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, 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 lowerdimensional representations of sparse hypergraphs, and identify a critical… CONTINUE READING
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