Bar-and-joint rigidity on the moment curve coincides with cofactor rigidity on a conic
Combinatorics
2023-03-16 v2
Abstract
We show that, for points along the moment curve, the bar-and-joint rigidity matroid and the hyperconnectivity matroid coincide, and that both coincide with the -cofactor rigidity of points along any (non-degenerate) conic in the plane. For hyperconnectivity in dimension two, having the points in the moment curve is no loss of generality. We also show that, restricted to bipartite graphs, the bar-and-joint rigidity matroid is freer than the hyperconnectivity matroid.
Keywords
Cite
@article{arxiv.2106.08923,
title = {Bar-and-joint rigidity on the moment curve coincides with cofactor rigidity on a conic},
author = {Luis Crespo Ruiz and Francisco Santos},
journal= {arXiv preprint arXiv:2106.08923},
year = {2023}
}
Comments
15 pages. Added details and some additional results, including suggestions from referees. This version has been accepted in "Combinatorial Theory"