Paradoxical motions and edge colorings

Georg Grasegger, 28 Nov 2022

Given a graph we consider its realizations in the plane and want to know whether they might be flexible while preserving edge lengths. A triangle graph for instance cannot be flexible because all edge lengths preserving motions are translations and rotations. The 4-cycle graph however has flexible realizations. It has been shown that the existence of motions can be related to a special coloring of the edges in two colors. Paradoxical motions appear when a graph is generically rigid but only for certain realizations we get something flexible. In this talk we see an overview of the existing results and show some topics of current research on paradoxical motions.