Vol. 90, No. 1, 1980

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When is a bipartite graph a rigid framework?

Ethan Bolker and Ben G. Roth

Vol. 90 (1980), No. 1, 27–44
Abstract

We find the dimension of the space of stresses for all realizations of the complete bipartite graph Km,n in Rd. That allows us to determine the infinitesimal rigidity or infinitesimal flexibility of such frameworks. The results lead both to the generic classification of Km,n in Rd 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
Authors
Ethan Bolker
Ben G. Roth