Year: 2011
Type: article
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 .
Source: Ars Mathematica Contemporanea
Authors: Ileana Streinu, Louis Theran
Institutions: Smith College, Temple University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2152473243