On the Rank Function of Generic Linearly Constrained Frameworks in $\mathbb{R}^2$

Abstract

We study the rank function of generic rigidity of bar-and-joint frameworks in R 2 such that some vertices are constrained to lie in some lines. The rigidity of such frameworks is characterised by Streinu and Theran [10]. In this paper we characterise the rank function of such frameworks in terms of vertex covers by extending Lovász and Yemini's characterisation of the rank function of the 2-dimensional generic bar-and-joint rigidity matroid [8].