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}
}