Natural Realizations of Sparsity Matroids

Authors

Ileana Streinu, Smith CollegeFollow
Louis Theran, Temple University

Document Type

Article

Publication Date

1-1-2011

Publication Title

Ars Mathematica Contemporanea

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 ≤ 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. Copyright © 2011 DMFA Slovenije.

Keywords

Combinatorial rigidity, Matroids, Sparse graphs and hypergraphs

Volume

4

Issue

1

First Page

141

Last Page

151

DOI

10.26493/1855-3974.197.461

ISSN

18553966

Rights

© 2011 DMFA Slovenije

Comments

Archived as published.

Recommended Citation

Streinu, Ileana and Theran, Louis, "Natural Realizations of Sparsity Matroids" (2011). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/308