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.

► We deal with generic bar-and-joint frameworks in three-space. ► We consider the case when their graph is a square, also called molecular graph. ► We show that if the graph is 7-vertex-connected then the framework is rigid. ► For molecular graphs this bound on the connectivity is best possible. ► This verifies a special case of a conjecture of Lovász and Yemini.