Bracing frameworks using edge colorings

Abstract

A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Choices of braces making a grid of squares infinitesimally rigid were characterized earlier using a bipartite graph constructed from the braced framework. We exploit the concept of NAC-colorings used to characterize the existence of flexible frameworks. In this way we give the results on bracing for a larger class of frameworks with every 4-cycle forming a parallelogram. This is a joint work with Georg Grasegger.