Rigid Components in Molecular Graphs

Rigid Components of Random Graphs

The planar rigidity problem asks, given a set of m pairwise distances among a set P of n unknown points, whether it is possible to reconstruct P , up to a finite set of possibilities (modulo rigid motions of the plane). The celebrated Maxwell-Laman Theorem from Rigidity Theory says that, generically, the rigidity problem has a combinatorial answer: the underlying combinatorial structure must co...

Highly connected molecular graphs are rigid in three dimensions

We show that every 7-vertex-connected molecular graph is generically rigid in three dimensions. This verifies a special case of a conjecture of Lovász and Yemini. For this family of graphs the bound is best possible.

Rigid and Deformable Components

In prior work we proposed a class of physically-based models suitable for animating /lezible objects in simulated physical environments {ll. Our original formulation works well in practice for models whose shapes are moderately to highly deformable, but it tends to become numerically ill-conditioned as we increase the rigidity of the models. The present paper develops an alternative formulation...

l 1 - Rigid Graphs

An l 1-graph is a graph whose nodes can be labeled by binary vectors in such a way that the Hamming distance between the binary addresses is, up to scale, the distance in the graph between the corresponding nodes. We show that many interesting graphs are l 1-rigid, i.e., that they admit an essentially unique such binary labeling.

Globally rigid frameworks and rigid tensegrity graphs in the plane