On Reconfiguring Tree Linkages: Trees can Lock
<|reference_start|>On Reconfiguring Tree Linkages: Trees can Lock: It has recently been shown that any simple (i.e. nonintersecting) polygonal chain in the plane can be reconfigured to lie on a straight line, and any simple polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two simple configurations that are not connected by a motion that preserves simplicity throughout the motion. Indeed, we prove that an $N$-link tree can have $2^{\Omega(N)}$ equivalence classes of configurations.<|reference_end|>
@article{biedl1999on,
    title={On Reconfiguring Tree Linkages: Trees can Lock},
    author={Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna
  Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint,
  Sue Whitesides},
    journal={arXiv preprint arXiv:cs/9910024},
    year={1999},
    number={SOCS-00.7},
    archivePrefix={arXiv},
    eprint={cs/9910024},
    primaryClass={cs.CG cs.DM}
}