Natural realizations of sparsity matroids

Ileana Streinu, Louis Theran


A hypergraph G with n vertices and m hyperedges with d endpoints each is (k, l)-sparse if for all sub-hypergraphs G' on n' vertices and m' edges, m'kn'l. For integers k and l satisfying 0 ≤ ldk − 1, this is known to be a linearly representable matroidal family. Motivated by problems in rigidity theory, we give a new linear representation theorem for the (k, l)-sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph G.


Matroids, combinatorial rigidity, sparse graphs and hypergraphs

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ISSN: 1855-3974

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