Corpus ID: 2054414

On reconfiguring tree linkages: Trees can lock

@article{Biedl1998OnRT,
  title={On reconfiguring tree linkages: Trees can lock},
  author={Therese C. Biedl and Erik D. Demaine and Martin L. Demaine and Sylvain Lazard and Anna Lubiw and Joseph O'Rourke and Steven M. Robbins and Ileana Streinu and Godfried T. Toussaint and Sue Whitesides},
  journal={ArXiv},
  year={1998},
  volume={cs.CG/9910024}
}
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 (N) equivalence classes of configurations. 

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