Natural realizations of sparsity matroids

Ileana Streinu, Louis Theran

Abstract


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.

Keywords


Matroids, combinatorial rigidity, sparse graphs and hypergraphs

Full Text:

PDF ABSTRACTS (EN/SI)


DOI: https://doi.org/10.26493/1855-3974.197.461

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications