2008/01/29 by D. G. Charlton, Charlton, David, Erik D. Demaine +7
Engineering · #Adhesion, Friction, and Surface Interactions #Advanced Materials and Mechanics #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.0801.4405
openalex publication_date 2008/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a counterexample to a conjecture of Poon [Poo06] that any orthogonal tree in two dimensions can always be flattened by a continuous motion that preserves edge lengths and avoids self-intersection. We show our example is locked by extending results on strongly locked self-touching linkages due to Connelly, Demaine and Rote [CDR02] to allow zero-length edges as defined in [ADG07], which may be of independent interest. Our results also yield a locked tree with only eleven edges, which is the smallest known example of a locked tree.