Geodesic
Natural realizations of sparsity matroids
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 141-151.

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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, m' ≤ kn' − l. For integers k and l satisfying 0 ≤ l ≤ 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.
DOI : 10.26493/1855-3974.197.461
Keywords: Matroids, combinatorial rigidity, sparse graphs and hypergraphs 
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Ileana Streinu; Louis Theran. Natural realizations of sparsity matroids. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 141-151. doi : 10.26493/1855-3974.197.461. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.197.461/

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