Natural realizations of sparsity matroids
DOI:
https://doi.org/10.26493/1855-3974.197.461Keywords:
Matroids, combinatorial rigidity, sparse graphs and hypergraphsAbstract
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.Downloads
Published
2011-02-16
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