Natural realizations of sparsity matroids

Authors

  • Ileana Streinu Smith College, United States
  • Louis Theran Temple University, United States

DOI:

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

Keywords:

Matroids, combinatorial rigidity, sparse graphs and hypergraphs

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.

Published

2011-02-16

Issue

Section

Articles