When is a bipartite graph a rigid framework?

Ethan Bolker and Ben G. Roth

Vol. 90 (1980), No. 1, 27–44

DOI: 10.2140/pjm.1980.90.27

Abstract

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.

Mathematical Subject Classification 2000

Primary: 57M15

Secondary: 05C10, 51F99, 51N10, 53A17, 57Q35

Milestones

Received: 28 August 1979

Published: 1 September 1980