English

On the Classification of Motions of Paradoxically Movable Graphs

Combinatorics 2021-02-05 v1 Robotics Algebraic Geometry Metric Geometry

Abstract

Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown recently that a graph has flexible edge lengths if and only if the graph has a special type of edge coloring called NAC-coloring. We address the question how to determine all possible proper flexible edge lengths from the set of all NAC-colorings of a graph. We do so using restrictions to 4-cycle subgraphs.

Keywords

Cite

@article{arxiv.2003.11416,
  title  = {On the Classification of Motions of Paradoxically Movable Graphs},
  author = {Georg Grasegger and Jan Legerský and Josef Schicho},
  journal= {arXiv preprint arXiv:2003.11416},
  year   = {2021}
}