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Natural realizations of sparsity matroids

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 Added by Louis Theran
 Publication date 2010
and research's language is English




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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, mle kn-l. For integers k and l satisfying 0le lle dk-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.



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