We say that a graph G is minimally globally rigid (in d dimensions) if it is globally rigid but G-e is not globally rigid for every edge e of G. We recently gave a tight upper bound on the number of edges in a minimally globally rigid graph. In particular, our result implies that a minimally globally rigid graph in d dimensions on at least d+3 vertices is flexible in d+1 dimensions.

In this talk I will discuss our proof, as well as a conjectured strengthening of our result that would give a new connection between d-dimensional global rigidity and (d+1)-dimensional rigidity. Joint work with Tibor Jordán.