When is a bipartite graph a rigid framework?

We find the dimension of the space of stresses for all realizations of the complete bipartite graph K m , n in R d . That allows us to determine the infinitesimal rigidity or infinitesimal flexibility of such frameworks. The results lead both to the generic classification of K m , n in R d and to a description of the realizations which deviate from the generic behavior. 1* Introduction* A framework in R d is a finite sequence Pi, ''' 9 Pv of points in R d called vertices together with a nonempty set E of sets {, j} such that 1 ^ i < j ^ v. Such a framework is a realization in R d LEMMA 2. If agB (respectively b$ A) then p a = 0 (respectively 7 6 = 0) for all stresses of K(A, B).