A Proof of the Molecular Conjecture

Abstract

We prove the Molecular Conjecture posed by Tay and Whiteley. This implies that a graph G can be realized as an infinitesimally rigid panel-hinge framework in ℝd by mapping each vertex to a rigid panel and each edge to a hinge if and only if, G contains, edge-disjoint spanning trees, where, G is the graph obtained from G by replacing each edge by parallel edges. © 2011 Springer Science+Business Media, LLC.